Kharazishvili, Alexander On uniform sets in Euclidean space \(\mathbf{R}^m\) and \(G\)-volumes. (English) Zbl 07887464 Trans. A. Razmadze Math. Inst. 178, No. 1, 161-163 (2024). MSC: 28A05 28A75 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Trans. A. Razmadze Math. Inst. 178, No. 1, 161--163 (2024; Zbl 07887464) Full Text: Link
Kharazishvili, Alexander Introduction to combinatorial methods in geometry. (English) Zbl 07873419 Boca Raton, FL: CRC Press (ISBN 978-1-032-59470-5/hbk; 978-1-003-45870-8/ebook). (2024). MSC: 51-01 52-01 05-01 PDFBibTeX XML Full Text: DOI
Kharazishvili, Alexander Quasi-invariant measures on topological groups and \(\omega\)-powers. (English) Zbl 07803149 Georgian Math. J. 31, No. 1, 69-78 (2024). MSC: 28A05 28D05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 31, No. 1, 69--78 (2024; Zbl 07803149) Full Text: DOI
Kharazishvili, Alexander On \(\pi\)-weights and extensions of invariant measures. (English) Zbl 1529.03263 Trans. A. Razmadze Math. Inst. 177, No. 2, 315-317 (2023). MSC: 03E75 03E15 28A05 28D05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Trans. A. Razmadze Math. Inst. 177, No. 2, 315--317 (2023; Zbl 1529.03263) Full Text: Link
Kharazishvili, Alexander On some version of random variables. (English) Zbl 1522.28001 Trans. A. Razmadze Math. Inst. 177, No. 1, 143-146 (2023). MSC: 28A05 60A10 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Trans. A. Razmadze Math. Inst. 177, No. 1, 143--146 (2023; Zbl 1522.28001) Full Text: Link
Kharazishvili, Alexander Nonmeasurable products of absolutely negligible sets in uncountable solvable groups. (English) Zbl 1523.28002 Georgian Math. J. 30, No. 3, 397-402 (2023). Reviewer: Miroslav Repický (Košice) MSC: 28A05 28A20 28C10 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 30, No. 3, 397--402 (2023; Zbl 1523.28002) Full Text: DOI
Kharazishvili, Alexander Notes on real analysis and measure theory. Fine properties of real sets and functions. (English) Zbl 1504.26003 Springer Monographs in Mathematics. Cham: Springer (ISBN 978-3-031-17032-4/hbk; 978-3-031-17035-5/pbk; 978-3-031-17032-4/ebook). xi, 253 p. (2022). Reviewer: Jaroslav Tišer (Praha) MSC: 26-02 28-02 54-02 03-02 22-02 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Notes on real analysis and measure theory. Fine properties of real sets and functions. Cham: Springer (2022; Zbl 1504.26003) Full Text: DOI
Kharazishvili, Alexander Sierpiński-Zygmund functions and \(\omega\)-powers. (English) Zbl 1509.54008 Trans. A. Razmadze Math. Inst. 176, No. 2, 281-284 (2022). Reviewer: Waldemar Sieg (Bydgoszcz) MSC: 54E52 26A30 54C30 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Trans. A. Razmadze Math. Inst. 176, No. 2, 281--284 (2022; Zbl 1509.54008) Full Text: Link
Kharazishvili, Alexander On rainbow isosceles \(n\)-simplexes. (English) Zbl 1498.52023 Georgian Math. J. 29, No. 4, 543-549 (2022). Reviewer: Maja Petrović (Beograd) MSC: 52B45 51M04 51M20 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 29, No. 4, 543--549 (2022; Zbl 1498.52023) Full Text: DOI
Kharazishvili, Alexander On a geometric statement of Ramsey type. (English) Zbl 07501803 Georgian Math. J. 29, No. 2, 229-232 (2022). MSC: 03E75 05D10 52C99 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 29, No. 2, 229--232 (2022; Zbl 07501803) Full Text: DOI
Kharazishvili, A. Mazurkiewicz sets of universal measure zero. (English) Zbl 07498920 Trans. A. Razmadze Math. Inst. 176, No. 1, 139-141 (2022). MSC: 03E50 28A05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Trans. A. Razmadze Math. Inst. 176, No. 1, 139--141 (2022; Zbl 07498920) Full Text: Link
Kharazishvili, A. An abstract version of sup-measurability. (English) Zbl 1497.28001 Trans. A. Razmadze Math. Inst. 176, No. 1, 135-138 (2022). MSC: 28A05 28D05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Trans. A. Razmadze Math. Inst. 176, No. 1, 135--138 (2022; Zbl 1497.28001) Full Text: Link
Kharazishvili, Alexander On nonmeasurable uniform subsets of the Euclidean plane. (English) Zbl 1495.28001 Trans. A. Razmadze Math. Inst. 175, No. 2, 285-286 (2021). MSC: 28A05 28D05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Trans. A. Razmadze Math. Inst. 175, No. 2, 285--286 (2021; Zbl 1495.28001) Full Text: Link
Kharazishvili, A. On the generalized nonmeasurability of some classical point sets. (English) Zbl 1496.03202 Trans. A. Razmadze Math. Inst. 175, No. 1, 151-153 (2021). MSC: 03E50 03E15 28A05 28E15 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Trans. A. Razmadze Math. Inst. 175, No. 1, 151--153 (2021; Zbl 1496.03202) Full Text: Link
Kharazishvili, A. On oscillations of real-valued functions. (English) Zbl 1485.54016 Trans. A. Razmadze Math. Inst. 175, No. 1, 63-67 (2021). MSC: 54C30 26A15 54D80 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Trans. A. Razmadze Math. Inst. 175, No. 1, 63--67 (2021; Zbl 1485.54016) Full Text: Link
Kharazishvili, Alexander On \(T_2\)-negligible \(S_2\)-absolutely nonmeasurable sets in the euclidean plane. (English) Zbl 1480.28002 Bull. TICMI 25, No. 1, 77-81 (2021). MSC: 28A05 28D05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Bull. TICMI 25, No. 1, 77--81 (2021; Zbl 1480.28002) Full Text: Link
Kharazishvili, Alexander On the generalized nonmeasurability of Vitali sets and Bernstein sets. (English) Zbl 1535.03250 Georgian Math. J. 28, No. 4, 575-579 (2021). MSC: 03E50 28A05 28E15 03E17 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 28, No. 4, 575--579 (2021; Zbl 1535.03250) Full Text: DOI
Kharazishvili, Alexander A measure zero set in the plane with absolutely nonmeasurable linear sections. (English) Zbl 1481.28003 Trans. A. Razmadze Math. Inst. 174, No. 3, 359-362 (2020). MSC: 28A05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Trans. A. Razmadze Math. Inst. 174, No. 3, 359--362 (2020; Zbl 1481.28003) Full Text: Link
Kharazishvili, Alexander Some remarks on Sierpiński-Zygmund functions in the strong sense. (English) Zbl 1464.26003 Georgian Math. J. 27, No. 4, 569-575 (2020). Reviewer: Piotr Sworowski (Bydgoszcz) MSC: 26A15 26A21 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 27, No. 4, 569--575 (2020; Zbl 1464.26003) Full Text: DOI
Kharazishvili, Alexander On finite sums of periodic functions. (English) Zbl 1439.26013 Georgian Math. J. 27, No. 2, 265-269 (2020). MSC: 26A03 26A12 28A20 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 27, No. 2, 265--269 (2020; Zbl 1439.26013) Full Text: DOI
Kharazishvili, Alexander On some applications of almost invariant sets. (English) Zbl 1470.22010 Bull. TICMI 23, No. 2, 115-124 (2019). MSC: 22F30 28A05 28D05 54H11 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Bull. TICMI 23, No. 2, 115--124 (2019; Zbl 1470.22010)
Kharazishvili, Alexander On projective functions with bad measurability properties. (English) Zbl 1472.28001 Bull. TICMI 23, No. 1, 77-81 (2019). MSC: 28A05 28A20 28D05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Bull. TICMI 23, No. 1, 77--81 (2019; Zbl 1472.28001) Full Text: Link
Kharazishvili, Alexander On orbits without the Baire property. (English) Zbl 1435.22016 Georgian Math. J. 26, No. 4, 625-628 (2019). Reviewer: Miroslav Repický (Košice) MSC: 22F30 28A05 28D05 54H11 54H15 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 26, No. 4, 625--628 (2019; Zbl 1435.22016) Full Text: DOI
Kharazishvili, Alexander On the Steinhaus property and ergodicity via the measure-theoretic density of sets. (English) Zbl 1423.28003 Real Anal. Exch. 44, No. 1, 217-228 (2019). Reviewer: Daniele Puglisi (Catania) MSC: 28A05 28D05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Real Anal. Exch. 44, No. 1, 217--228 (2019; Zbl 1423.28003) Full Text: DOI Euclid
Kharazishvili, Alexander Some remarks on the Steinhaus property for invariant extensions of the Lebesgue measure. (English) Zbl 1414.28004 Eur. J. Math. 5, No. 1, 81-90 (2019). Reviewer: Daniele Puglisi (Catania) MSC: 28A05 28D05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Eur. J. Math. 5, No. 1, 81--90 (2019; Zbl 1414.28004) Full Text: DOI
Kharazishvili, Alexander On generalized measurability properties of certain projective sets. (English) Zbl 1408.28002 Bull. TICMI 22, No. 1, 59-64 (2018). MSC: 28A05 28A20 28D05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Bull. TICMI 22, No. 1, 59--64 (2018; Zbl 1408.28002) Full Text: EMIS Link
Kharazishvili, Alexander A note on the Borel types of some small sets. (English) Zbl 1400.28003 Georgian Math. J. 25, No. 3, 419-425 (2018). MSC: 28A05 28C10 28D05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 25, No. 3, 419--425 (2018; Zbl 1400.28003) Full Text: DOI
Kharazishvili, Alexander A note on the uniqueness property for Borel \(G\)-measures. (English) Zbl 1400.28002 Real Anal. Exch. 43, No. 1, 223-234 (2018). Reviewer: Daniele Puglisi (Catania) MSC: 28A05 28D05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Real Anal. Exch. 43, No. 1, 223--234 (2018; Zbl 1400.28002)
Kharazishvili, Alexander On some classes of negligible subsets of the Euclidean plane. (English) Zbl 1384.28004 Georgian Math. J. 25, No. 1, 41-46 (2018). MSC: 28A05 28D05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 25, No. 1, 41--46 (2018; Zbl 1384.28004) Full Text: DOI
Kharazishvili, Alexander Strange functions in real analysis. 3rd edition. (English) Zbl 1375.26004 Boca Raton, FL: CRC Press (ISBN 978-1-4987-7314-0/hbk; 978-1-4987-7315-7/ebook). xiii, 426 p. (2018). MSC: 26-02 26A27 26A30 28A05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Strange functions in real analysis. 3rd edition. Boca Raton, FL: CRC Press (2018; Zbl 1375.26004) Full Text: Link
Kharazishvili, Alexander On Mazurkiewicz sets from the measure-theoretical point of view. (English) Zbl 1373.28001 Bull. TICMI 21, No. 1, 45-54 (2017). MSC: 28A05 28D05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Bull. TICMI 21, No. 1, 45--54 (2017; Zbl 1373.28001)
Kharazishvili, Alexander A characterization of sets containing absolutely nonmeasurable subsets. (English) Zbl 1364.28001 Georgian Math. J. 24, No. 2, 211-215 (2017). MSC: 28A05 28C10 28D05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 24, No. 2, 211--215 (2017; Zbl 1364.28001) Full Text: DOI
Kharazishvili, Alexander Acute triangles in the context of the illumination problem. (English) Zbl 1474.52016 God. Sofiĭ. Univ., Fak. Mat. Inform. 103, 39-44 (2016). MSC: 52B05 52B11 52C10 PDFBibTeX XMLCite \textit{A. Kharazishvili}, God. Sofiĭ. Univ., Fak. Mat. Inform. 103, 39--44 (2016; Zbl 1474.52016) Full Text: Link
Kharazishvili, Alexander Absolute null subsets of the plane with bad orthogonal projections. (English) Zbl 1384.28003 Real Anal. Exch. 41(2015-2016), No. 1, 233-244 (2016). Reviewer: Ryszard Pawlak (Łódź) MSC: 28A05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Real Anal. Exch. 41, No. 1, 233--244 (2016; Zbl 1384.28003) Full Text: DOI Euclid
Kharazishvili, A. On bijective continuous images of absolute null sets. (English) Zbl 1379.28001 Ukr. Math. J. 67, No. 8, 1277-1282 (2016) and Ukr. Mat. Zh. 67, No. 8, 1134-1138 (2015). MSC: 28A05 54H05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Ukr. Math. J. 67, No. 8, 1277--1282 (2016; Zbl 1379.28001) Full Text: DOI Link
Kharazishvili, Alexander Measurability properties of Mazurkiewicz sets. (English) Zbl 1362.28003 Bull. TICMI 20, No. 2, 44-46 (2016). MSC: 28A05 28C10 28D05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Bull. TICMI 20, No. 2, 44--46 (2016; Zbl 1362.28003)
Kharazishvili, Alexander On negligible and absolutely nonmeasurable subsets of uncountable solvable groups. (English) Zbl 1350.28013 Trans. A. Razmadze Math. Inst. 170, No. 1, 69-74 (2016). MSC: 28C10 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Trans. A. Razmadze Math. Inst. 170, No. 1, 69--74 (2016; Zbl 1350.28013) Full Text: DOI OA License
Kharazishvili, Alexander On the cardinal number of the family of all invariant extensions of a nonzero \(\sigma\)-finite invariant measure. (English) Zbl 1354.28001 Trans. A. Razmadze Math. Inst. 170, No. 2, 200-204 (2016). MSC: 28A12 03E75 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Trans. A. Razmadze Math. Inst. 170, No. 2, 200--204 (2016; Zbl 1354.28001) Full Text: DOI OA License
Kharazishvili, Alexander On the difference between a Vitali-Bernstein selector and a partial Vitali-Bernstein selector. (English) Zbl 1346.28002 Georgian Math. J. 23, No. 3, 387-391 (2016). MSC: 28A05 28D05 03E75 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 23, No. 3, 387--391 (2016; Zbl 1346.28002) Full Text: DOI
Kharazishvili, Alexander A partition of an uncountable solvable group into three negligible subsets. (English) Zbl 1336.28011 Bull. TICMI 19, No. 1, 37-44 (2015). Reviewer: Hans Weber (Udine) MSC: 28D05 28C99 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Bull. TICMI 19, No. 1, 37--44 (2015; Zbl 1336.28011)
Kharazishvili, A. On inscribed and circumscribed convex polyhedra. (English) Zbl 1333.52013 Proc. A. Razmadze Math. Inst. 167, 123-129 (2015). Reviewer: Matthieu Jacquemet (Nashville) MSC: 52B05 52B10 52B11 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Proc. A. Razmadze Math. Inst. 167, 123--129 (2015; Zbl 1333.52013)
Kharazishvili, Alexander Three-colorings of the Euclidean plane and associated triangles of a prescribed type. (English) Zbl 1320.05043 Georgian Math. J. 22, No. 3, 393-396 (2015). MSC: 05C15 05C05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 22, No. 3, 393--396 (2015; Zbl 1320.05043) Full Text: DOI
Kharazishvili, Alexander On the cardinalities of \(at\)-sets in a real Hilbert space. (English) Zbl 1339.52012 Georgian Math. J. 22, No. 2, 259-263 (2015). Reviewer: Franka Miriam Brueckler (Zagreb) MSC: 52C10 46C05 03E10 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 22, No. 2, 259--263 (2015; Zbl 1339.52012) Full Text: DOI
Kharazishvili, Alexander B. Set theoretical aspects of real analysis. (English) Zbl 1298.28001 Monographs and Research Notes in Mathematics. Boca Raton, FL: CRC Press (ISBN 978-1-4822-4201-0/hbk; 978-1-4822-4202-7/ebook). xxii, 433 p. (2015). Reviewer: Peter Massopust (München) MSC: 28-01 00A05 03E75 26-01 PDFBibTeX XMLCite \textit{A. B. Kharazishvili}, Set theoretical aspects of real analysis. Boca Raton, FL: CRC Press (2015; Zbl 1298.28001) Full Text: DOI
Kharazishvili, A. B. On partitions of the real line into continuum many thick subsets. (English) Zbl 1323.28002 Real Anal. Exch. 39(2013-2014), No. 2, 459-468 (2014). Reviewer: K. P. Hart (Delft) MSC: 28A05 28D05 03E25 PDFBibTeX XMLCite \textit{A. B. Kharazishvili}, Real Anal. Exch. 39, No. 2, 459--468 (2014; Zbl 1323.28002) Full Text: DOI Euclid
Kharazishvili, A. To the existence of projective absolutely nonmeasurable functions. (English) Zbl 1321.28005 Proc. A. Razmadze Math. Inst. 166, 95-102 (2014). MSC: 28A05 28D05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Proc. A. Razmadze Math. Inst. 166, 95--102 (2014; Zbl 1321.28005)
Kharazishvili, A. B. On countable almost invariant partitions of \(G\)-spaces. (English) Zbl 1347.28002 Ukr. Math. J. 66, No. 4, 572-579 (2014) and Ukr. Mat. Zh. 66, No. 4, 510-517 (2014). MSC: 28A05 28D05 PDFBibTeX XMLCite \textit{A. B. Kharazishvili}, Ukr. Math. J. 66, No. 4, 572--579 (2014; Zbl 1347.28002) Full Text: DOI
Kharazishvili, Alexander A characterization of uncountable sets in terms of their self-mappings and large invariant subsets. (English) Zbl 1337.03072 Georgian Math. J. 21, No. 3, 297-302 (2014). MSC: 03E10 03E20 03E25 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 21, No. 3, 297--302 (2014; Zbl 1337.03072) Full Text: DOI
Kharazishvili, A. On a theorem of Luzin and Sierpinski. (English) Zbl 1296.28004 Proc. A. Razmadze Math. Inst. 164, 109-115 (2014). MSC: 28A05 28D05 03E25 03E30 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Proc. A. Razmadze Math. Inst. 164, 109--115 (2014; Zbl 1296.28004) Full Text: Link
Kharazishvili, A. On measurability properties of Bernstein sets. (English) Zbl 1296.28003 Proc. A. Razmadze Math. Inst. 164, 63-70 (2014). MSC: 28A05 28D05 03E25 03E30 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Proc. A. Razmadze Math. Inst. 164, 63--70 (2014; Zbl 1296.28003) Full Text: Link
Kharazishvili, Alexander B. On some real-valued step-functions with strange measurability properties. (English) Zbl 1286.28002 Georgian Math. J. 21, No. 1, 83-87 (2014). MSC: 28A20 28D05 22B99 PDFBibTeX XMLCite \textit{A. B. Kharazishvili}, Georgian Math. J. 21, No. 1, 83--87 (2014; Zbl 1286.28002) Full Text: DOI
Kharazishvili, Alexander B. Additive properties of certain classes of pathological functions. (English) Zbl 1303.28001 Real Anal. Exch. 38(2012-2013), No. 2, 475-486 (2013). Reviewer: Enrico Zoli (Firenze) MSC: 28A05 28D05 PDFBibTeX XMLCite \textit{A. B. Kharazishvili}, Real Anal. Exch. 38, No. 2, 475--486 (2013; Zbl 1303.28001) Full Text: DOI Euclid
Kharazishvili, A. B. On absolutely nonmeasurable homomorphisms of commutative groups. (English) Zbl 1299.28002 Stud. Sci. Math. Hung. 50, No. 3, 287-295 (2013). Reviewer: Hans Weber (Udine) MSC: 28A20 28D05 PDFBibTeX XMLCite \textit{A. B. Kharazishvili}, Stud. Sci. Math. Hung. 50, No. 3, 287--295 (2013; Zbl 1299.28002) Full Text: DOI
Kharazishvili, A. On some pathological homomorphisms of uncountable commutative groups. (English) Zbl 1294.28003 Proc. A. Razmadze Math. Inst. 162, 136-140 (2013). Reviewer: K. P. Hart (Delft) MSC: 28A20 20K30 28C10 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Proc. A. Razmadze Math. Inst. 162, 136--140 (2013; Zbl 1294.28003)
Kharazishvili, A. Some unsolved problems in measure theory. (English) Zbl 1290.28003 Proc. A. Razmadze Math. Inst. 162, 59-77 (2013). MSC: 28A05 28D05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Proc. A. Razmadze Math. Inst. 162, 59--77 (2013; Zbl 1290.28003)
Kharazishvili, Alexander On the measurability properties of well-orderings. (English) Zbl 1277.28001 Georgian Math. J. 20, No. 3, 533-545 (2013). MSC: 28A05 28D05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 20, No. 3, 533--545 (2013; Zbl 1277.28001) Full Text: DOI
Kharazishvili, Alexander Sums of absolutely nonmeasurable functions. (English) Zbl 1270.28002 Georgian Math. J. 20, No. 2, 271-282 (2013). MSC: 28A05 28D05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 20, No. 2, 271--282 (2013; Zbl 1270.28002) Full Text: DOI
Kharazishvili, Alexander Some geometric consequences of Ramsey’s combinatorial theorem. (English) Zbl 1323.52003 Bull. TICMI 16, No. 1, 34-42 (2012). MSC: 52A15 52B05 52B10 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Bull. TICMI 16, No. 1, 34--42 (2012; Zbl 1323.52003) Full Text: EMIS
Kharazishvili, Alexander B. A large group of nonmeasurable additive functions. (English) Zbl 1276.28003 Real Anal. Exch. 37(2011-2012), No. 2, 467-476 (2012). Reviewer: Miroslav Repický (Košice) MSC: 28A05 28D05 03E50 PDFBibTeX XMLCite \textit{A. B. Kharazishvili}, Real Anal. Exch. 37, No. 2, 467--476 (2012; Zbl 1276.28003) Full Text: DOI Euclid
Kharazishvili, A. Some properties of \(at\)-sets and \(ot\)-sets in a Hilbert space. (English) Zbl 1276.05123 Proc. A. Razmadze Math. Inst. 159, 147-151 (2012). MSC: 05D05 52A15 52B05 52B10 52B35 52B45 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Proc. A. Razmadze Math. Inst. 159, 147--151 (2012; Zbl 1276.05123)
Kharazishvili, Alexander Some topologic-geometrical properties of external bisectors of a triangle. (English) Zbl 1266.51022 Georgian Math. J. 19, No. 4, 697-704 (2012). Reviewer: Georgi Hristov Georgiev (Shumen) MSC: 51M04 51M15 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 19, No. 4, 697--704 (2012; Zbl 1266.51022) Full Text: DOI
Kharazishvili, A. B. Ergodic measures and the definability of subgroups via normal extensions of such measures. (English) Zbl 1265.28036 Theory Stoch. Process. 18, No. 1, 58-64 (2012). MSC: 28C10 28D05 22B99 PDFBibTeX XMLCite \textit{A. B. Kharazishvili}, Theory Stoch. Process. 18, No. 1, 58--64 (2012; Zbl 1265.28036)
Kharazishvili, Alexander Measurable and nonmeasurable sets with homogeneous sections. (English) Zbl 1246.28002 Georgian Math. J. 19, No. 2, 247-258 (2012). MSC: 28A05 28A20 28A35 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 19, No. 2, 247--258 (2012; Zbl 1246.28002) Full Text: DOI
Kharazishvili, A. On finite and infinite ot-sets. (English) Zbl 1291.05202 Bull. TICMI 15, 27-34 (2011). MSC: 05D10 03E50 28A05 52A10 52A20 52B05 52C10 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Bull. TICMI 15, 27--34 (2011; Zbl 1291.05202) Full Text: EMIS
Kharazishvili, Alexander B. Some remarks concerning monotone and continuous restrictions of real-valued functions. (English) Zbl 1282.26004 Proc. A. Razmadze Math. Inst. 157, 11-21 (2011). MSC: 26A15 26A48 26A21 PDFBibTeX XMLCite \textit{A. B. Kharazishvili}, Proc. A. Razmadze Math. Inst. 157, 11--21 (2011; Zbl 1282.26004)
Kharazishvili, Alexander A note on algebraic convex curves of constant width. (English) Zbl 1236.52002 Georgian Math. J. 18, No. 4, 727-733 (2011). Reviewer: T. D. Narang (Amritsar) MSC: 52A10 14H50 52A27 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 18, No. 4, 727--733 (2011; Zbl 1236.52002) Full Text: DOI
Kharazishvili, A. Some discrete geometric structures and associated algorithms. (English) Zbl 1235.52022 Proc. A. Razmadze Math. Inst. 155, 138-144 (2011). Reviewer: Dimitris P. Vartziotis (Ioannina) MSC: 52B45 52A15 52B05 52B10 52B35 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Proc. A. Razmadze Math. Inst. 155, 138--144 (2011; Zbl 1235.52022)
Kharazishvili, A. On ordinary differential equations with bad right-hand sides. (English) Zbl 1235.34032 Proc. A. Razmadze Math. Inst. 155, 135-137 (2011). MSC: 34A12 26B30 28A20 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Proc. A. Razmadze Math. Inst. 155, 135--137 (2011; Zbl 1235.34032)
Kharazishvili, A. B. Measurability properties of Vitali sets. (English) Zbl 1232.28003 Am. Math. Mon. 118, No. 8, 693-703 (2011). Reviewer: Hans Weber (Udine) MSC: 28A05 28A12 PDFBibTeX XMLCite \textit{A. B. Kharazishvili}, Am. Math. Mon. 118, No. 8, 693--703 (2011; Zbl 1232.28003) Full Text: DOI
Kharazishvili, Alexander On a relationship between absolutely nonmeasurable functions and Sierpiński-Zygmund functions. (English) Zbl 1230.54019 Georgian Math. J. 18, No. 2, 249-258 (2011). Reviewer: Luca Motto Ros (Freiburg im Breisgau) MSC: 54C30 54H05 28A05 28E15 03E15 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 18, No. 2, 249--258 (2011; Zbl 1230.54019) Full Text: DOI
Kharazishvili, A. B. A combinatorial problem on translation-invariant extensions of the Lebesgue measure. (English) Zbl 1217.28002 Expo. Math. 29, No. 1, 150-158 (2011). MSC: 28A05 28D05 PDFBibTeX XMLCite \textit{A. B. Kharazishvili}, Expo. Math. 29, No. 1, 150--158 (2011; Zbl 1217.28002) Full Text: DOI
Kharazishvili, A. B. Some combinatorial problems on the measurability of functions with respect to invariant extensions of the Lebesgue measure. (English) Zbl 1226.28002 Acta Univ. Carol., Math. Phys. 51, Suppl., 57-65 (2010). MSC: 28A05 28A20 28D05 PDFBibTeX XMLCite \textit{A. B. Kharazishvili}, Acta Univ. Carol., Math. Phys. 51, 57--65 (2010; Zbl 1226.28002) Full Text: EuDML Link
Kharazishvili, A. On nonmeasurable unions of measure zero sections of plane sets. (English) Zbl 1215.28002 Proc. A. Razmadze Math. Inst. 154, 137-143 (2010). MSC: 28A05 28E15 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Proc. A. Razmadze Math. Inst. 154, 137--143 (2010; Zbl 1215.28002)
Kharazishvili, Alexander B. On almost measurable real-valued functions. (English) Zbl 1240.28001 Stud. Sci. Math. Hung. 47, No. 2, 257-266 (2010). Reviewer: George Stoica (Saint John) MSC: 28A05 28D05 PDFBibTeX XMLCite \textit{A. B. Kharazishvili}, Stud. Sci. Math. Hung. 47, No. 2, 257--266 (2010; Zbl 1240.28001) Full Text: DOI
Kharazishvili, Alexander On a relationship between the measurability and continuity of real-valued functions. (English) Zbl 1204.28001 Georgian Math. J. 17, No. 4, 649-661 (2010). MSC: 28A05 28A20 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 17, No. 4, 649--661 (2010; Zbl 1204.28001) Full Text: DOI
Kharazishvili, A. B.; Tetunashvili, T. Sh. On some coverings of the Euclidean plane with pairwise congruent circles. (English) Zbl 1218.52019 Am. Math. Mon. 117, No. 5, 414-423 (2010). Reviewer: A. E. Litvak (Edmonton) MSC: 52C15 05B40 PDFBibTeX XMLCite \textit{A. B. Kharazishvili} and \textit{T. Sh. Tetunashvili}, Am. Math. Mon. 117, No. 5, 414--423 (2010; Zbl 1218.52019) Full Text: DOI
Kharazishvili, A. Piecewise affine approximations of continuous functions of several variables and Gale polyhedra. (English) Zbl 1197.41022 Proc. A. Razmadze Math. Inst. 152, 133-140 (2010). MSC: 41A45 41A63 52B35 52B45 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Proc. A. Razmadze Math. Inst. 152, 133--140 (2010; Zbl 1197.41022)
Kharazishvili, A. B. On some applications of set-theoretical methods in Euclidean geometry. (English) Zbl 1268.03078 Bull. TICMI 13, 12-20 (2009). MSC: 03E75 03E25 03E50 51M04 52A20 PDFBibTeX XMLCite \textit{A. B. Kharazishvili}, Bull. TICMI 13, 12--20 (2009; Zbl 1268.03078) Full Text: EMIS
Kharazishvili, A. On sets with homogeneous linear sections. (English) Zbl 1195.28002 Proc. A. Razmadze Math. Inst. 151, 124-128 (2009). MSC: 28A05 28D05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Proc. A. Razmadze Math. Inst. 151, 124--128 (2009; Zbl 1195.28002)
Kharazishvili, A. Finite families of negligible sets and invariant extensions of the Lebesgue measure. (English) Zbl 1193.28002 Proc. A. Razmadze Math. Inst. 151, 119-123 (2009). MSC: 28A05 28D05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Proc. A. Razmadze Math. Inst. 151, 119--123 (2009; Zbl 1193.28002)
Kharazishvili, Alexander On nonmeasurable functions of two variables and iterated integrals. (English) Zbl 1182.28006 Georgian Math. J. 16, No. 4, 705-710 (2009). MSC: 28A05 28D05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 16, No. 4, 705--710 (2009; Zbl 1182.28006)
Kharazishvili, A. B. Metrical transitivity and nonseparable extensions of invariant measures. (English) Zbl 1184.28006 Taiwanese J. Math. 13, No. 3, 943-949 (2009). Reviewer: Tamás Mátrai (Highland Park) MSC: 28A60 28A05 28D05 28D15 PDFBibTeX XMLCite \textit{A. B. Kharazishvili}, Taiwanese J. Math. 13, No. 3, 943--949 (2009; Zbl 1184.28006) Full Text: DOI
Kharazishvili, A. B. On thick subgroups of uncountable \(\sigma \)-compact locally compact commutative groups. (English) Zbl 1177.22002 Topology Appl. 156, No. 14, 2364-2369 (2009). Reviewer: K. P. Hart (Delft) MSC: 22B05 28C10 28A05 28D05 PDFBibTeX XMLCite \textit{A. B. Kharazishvili}, Topology Appl. 156, No. 14, 2364--2369 (2009; Zbl 1177.22002) Full Text: DOI
Kharazishvili, Alexander Topics in measure theory and real analysis. (English) Zbl 1241.28001 Atlantis Studies in Mathematics 2. Hackensack, NJ: World Scientific; Paris: Atlantis Press (ISBN 978-90-78677-20-8/hbk). xiv, 461 p. (2009). MSC: 28-02 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Topics in measure theory and real analysis. Hackensack, NJ: World Scientific; Paris: Atlantis Press (2009; Zbl 1241.28001)
Kharazishvili, A. B. On sums of real-valued functions with extremely thick graphs. (English) Zbl 1177.28003 Expo. Math. 27, No. 2, 161-169 (2009). Reviewer: Jörg D. Brendle (Kobe) MSC: 28A05 28D05 28A60 PDFBibTeX XMLCite \textit{A. B. Kharazishvili}, Expo. Math. 27, No. 2, 161--169 (2009; Zbl 1177.28003) Full Text: DOI
Kharazishvili, Alexander B. On a bad descriptive structure of Minkowski’s sum of certain small sets in a topological vector space. (English) Zbl 1224.28002 Theory Stoch. Process. 14, No. 2, 35-41 (2008). MSC: 28A05 28C10 28D05 PDFBibTeX XMLCite \textit{A. B. Kharazishvili}, Theory Stoch. Process. 14, No. 2, 35--41 (2008; Zbl 1224.28002)
Kharazishvili, Alexander B.; Kirtadze, Aleks P. On measurability of algebraic sums of small sets. (English) Zbl 1199.28004 Stud. Sci. Math. Hung. 45, No. 3, 433-442 (2008). Reviewer: Beloslav Reičan (Banska Bystrica) MSC: 28A05 28D05 03E25 PDFBibTeX XMLCite \textit{A. B. Kharazishvili} and \textit{A. P. Kirtadze}, Stud. Sci. Math. Hung. 45, No. 3, 433--442 (2008; Zbl 1199.28004) Full Text: DOI
Kharazishvili, Alexander B. Some properties of step-functions connected with extension of measures. (English) Zbl 1181.28001 Acta Univ. Carol., Math. Phys. 49, No. 2, 57-65 (2008). MSC: 28A05 28D05 PDFBibTeX XMLCite \textit{A. B. Kharazishvili}, Acta Univ. Carol., Math. Phys. 49, No. 2, 57--65 (2008; Zbl 1181.28001) Full Text: EuDML
Kharazishvili, Alexander; Tetunashvili, Tengiz On some combinatorial problems concerning geometrical realizations of finite and infinite families of sets. (English) Zbl 1166.52005 Georgian Math. J. 15, No. 4, 665-675 (2008). Reviewer: A. C. Thompson (Halifax) MSC: 52A10 52A35 52B05 PDFBibTeX XMLCite \textit{A. Kharazishvili} and \textit{T. Tetunashvili}, Georgian Math. J. 15, No. 4, 665--675 (2008; Zbl 1166.52005)
Kharazishvili, A.; Tetunashvili, T. Combinatorial properties of families of sets and Euler-Venn diagrams. (English) Zbl 1221.52003 Proc. A. Razmadze Math. Inst. 146, 115-119 (2008). MSC: 52A10 52A35 52B05 PDFBibTeX XMLCite \textit{A. Kharazishvili} and \textit{T. Tetunashvili}, Proc. A. Razmadze Math. Inst. 146, 115--119 (2008; Zbl 1221.52003)
Kharazishvili, Alexander On absolutely nonmeasurable sets and functions. (English) Zbl 1155.28001 Georgian Math. J. 15, No. 2, 317-325 (2008). Reviewer: Yuang-Ling Ye (Guangzhou) MSC: 28A05 28D05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 15, No. 2, 317--325 (2008; Zbl 1155.28001)
Kharazishvili, A. B. A nonseparable extension of the Lebesgue measure without new nullsets. (English) Zbl 1149.28002 Real Anal. Exch. 33(2007-2008), No. 1, 259-268 (2008). Reviewer: Petr Holický (Praha) MSC: 28A05 28D05 PDFBibTeX XMLCite \textit{A. B. Kharazishvili}, Real Anal. Exch. 33, No. 1, 259--268 (2008; Zbl 1149.28002) Full Text: DOI
Kharazishvili, A. Some aspects of the measure extension problem. (English) Zbl 1167.28300 Proc. A. Razmadze Math. Inst. 143, 73-78 (2007). Reviewer: Ákos Császár (Budapest) MSC: 28A12 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Proc. A. Razmadze Math. Inst. 143, 73--78 (2007; Zbl 1167.28300) Full Text: Link
Kharazishvili, A. Ergodic components and nonseparable extensions of invariant measures. (English) Zbl 1151.28016 Proc. A. Razmadze Math. Inst. 145, No. 2, 95-99 (2007). Reviewer: K. P. Hart (Delft) MSC: 28C10 28A05 28D05 03E10 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Proc. A. Razmadze Math. Inst. 145, No. 2, 95--99 (2007; Zbl 1151.28016)
Kharazishvili, Alexander Some combinatorial properties of finite line-systems in the Euclidean plane. (English) Zbl 1139.05009 Georgian Math. J. 14, No. 4, 681-686 (2007). MSC: 05B25 05A15 52C30 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 14, No. 4, 681--686 (2007; Zbl 1139.05009)
Kharazishvili, Alexander; Kirtadze, Aleks On nonmeasurable subgroups of uncountable solvable groups. (English) Zbl 1132.28300 Georgian Math. J. 14, No. 3, 435-444 (2007). MSC: 28A05 28D05 PDFBibTeX XMLCite \textit{A. Kharazishvili} and \textit{A. Kirtadze}, Georgian Math. J. 14, No. 3, 435--444 (2007; Zbl 1132.28300)
Kharazishvili, A. B.; Kirtadze, A. P. On extensions of partial functions. (English) Zbl 1132.26303 Expo. Math. 25, No. 4, 345-353 (2007). MSC: 26A15 26A21 26A30 28B20 PDFBibTeX XMLCite \textit{A. B. Kharazishvili} and \textit{A. P. Kirtadze}, Expo. Math. 25, No. 4, 345--353 (2007; Zbl 1132.26303) Full Text: DOI
Kharazishvili, Alexander On the measurability of additive functionals. (English) Zbl 1131.28001 Georgian Math. J. 14, No. 1, 135-143 (2007). MSC: 28A05 28D05 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 14, No. 1, 135--143 (2007; Zbl 1131.28001)
Kharazishvili, A. B.; Kirtadze, A. P. On weakly metrically transitive measures and nonmeasurable sets. (English) Zbl 1132.28001 Real Anal. Exch. 32(2006-2007), No. 2, 553-562 (2007). Reviewer: Miroslav Repický (Košice) MSC: 28A05 28D05 PDFBibTeX XMLCite \textit{A. B. Kharazishvili} and \textit{A. P. Kirtadze}, Real Anal. Exch. 32, No. 2, 553--562 (2007; Zbl 1132.28001) Full Text: DOI
Kharazishvili, Alexander On decompositions of a cube into cubes and simplexes. (English) Zbl 1126.52005 Georgian Math. J. 13, No. 2, 285-290 (2006). Reviewer: Horst Martini (Chemnitz) MSC: 52A15 52B05 52B10 PDFBibTeX XMLCite \textit{A. Kharazishvili}, Georgian Math. J. 13, No. 2, 285--290 (2006; Zbl 1126.52005)