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Cesari-Weierstrass surface integrals and lower k-area. (English) Zbl 0232.28011

MSC:
28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures
28A75 Length, area, volume, other geometric measure theory
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References:
[1] J.C. Breckenridge , Burkill-Cesari integrals of quasi additive interval functions . To appear. MR 313482 | Zbl 0226.28011 · Zbl 0226.28011 · doi:10.2140/pjm.1971.37.635
[2] J.C. Breckenridge , Significant sets in surface area theory . To appear. · Zbl 0232.28011
[3] L. Cesari , La nozione di integrale 80pra una superficie in forma parametrica . Ann. Scuola Norm. Sup. Pisa ( 2 ), vol 13 ( 1944 ), pp. 77 - 117 . Numdam | MR 24510 | Zbl 0029.29102 · Zbl 0029.29102 · numdam:ASNSP_1948_2_13_1-4_77_0 · eudml:83054
[4] L. Cesari , L’area di Lebesgue come una misura . Rend. Mat. Appl. Roma , vol. 14 ( 1955 ), pp. 655 - 673 . MR 73680 | Zbl 0065.28801 · Zbl 0065.28801
[5] L. Cesari , Surface Area , Princeton University Press ( 1956 ). MR 74500 | Zbl 0073.04101 · Zbl 0073.04101
[6] L. Cesari , Quasi additive set functions and the concept of integral over a variety . Trans. Amer. Math. Soc. vol. 102 ( 1962 ), pp. 94 - 113 . MR 142723 | Zbl 0115.26902 · Zbl 0115.26902 · doi:10.2307/1993882
[7] L. Cesari , Extension problem for quasi additive set functions and Radon-Nikodym derivatives , Trans. Amer. Math. Soc. vol. 102 ( 1962 ), pp. 114 - 146 . MR 142724 | Zbl 0115.27001 · Zbl 0115.27001 · doi:10.2307/1993883
[8] L. Cesari and L.H. Turner , Surface integrals and Radon-Nikodym derivatives , Rend. Circ. Mat. Palermo. vol. 7 ( 1958 ), pp. 143 - 154 . MR 104781 | Zbl 0087.27103 · Zbl 0087.27103 · doi:10.1007/BF02854524
[9] H. Federer , Currents and area , Trans. Amer. Math. Soc. vol. 98 ( 1961 ), pp. 204 - 233 . MR 123682 | Zbl 0187.31302 · Zbl 0187.31302 · doi:10.2307/1993493
[10] R. Gariepy , Current valued measures and Geöcze area . Thesis. Wayne State University ( 1969 ). · Zbl 0235.28014
[11] J.H. Michael , The convergence of measures on parametric surfaces , Trans. Amer. Math. Soc. vol. 107 ( 1963 ), pp. 140 - 152 . MR 146352 | Zbl 0138.03602 · Zbl 0138.03602 · doi:10.2307/1993873
[12] T. Nishiura , The Geöcze k-area and a cylindrical property . Proc. Amer. Math. Soc. vol. 12 ( 1961 ), pp. 795 .800. MR 125941 | Zbl 0113.04202 · Zbl 0113.04202 · doi:10.2307/2034878
[13] T. Nishiura , The Geöcze k-area and flat mappings , Rend. Ciro. Mat. Palermo. vol. 11 ( 1962 ), pp. 105 - 125 . MR 148855 | Zbl 0111.05702 · Zbl 0111.05702 · doi:10.1007/BF02849429
[14] T. Nishiura , Integrals over a product variety and Fubini theorems , Rend. Circ. Mat. Palermo. vol. 14 ( 1965 ), pp. 207 - 236 . MR 197685 | Zbl 0154.05302 · Zbl 0154.05302 · doi:10.1007/BF02847721
[15] T. Nishiura , Area measure and Radó’s lower area . To appear. Zbl 0226.28012 · Zbl 0226.28012 · doi:10.2307/1996016
[16] T. Radó , Length and Area . Amer. Math. Soc. Coll. Publ. , 30 . ( 1948 ). MR 24511 | Zbl 0033.17002 · Zbl 0033.17002
[17] T. Radó and P.V. Reicheldehfer , Continuous Transformations in Analysis . Berlin , Springer ( 1955 ). · Zbl 0067.03506
[18] G. Warner , The Burkill-Cesari integral . Duke Math. Journal. vol. 35 ( 1968 ), pp. 61 - 78 . Article | MR 219690 | Zbl 0165.06702 · Zbl 0165.06702 · doi:10.1215/S0012-7094-68-03507-2 · minidml.mathdoc.fr
[19] G. Warner , The generalized Weierstrass-type integral \int \? (\zeta , \varphi ) , Ann. Scuola Norm. Sup. Pisa ( 2 ). vol. 22 ( 1968 ), pp. 163 - 192 . Numdam | Zbl 0174.09203 · Zbl 0174.09203 · numdam:ASNSP_1968_3_22_2_163_0 · eudml:83455
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