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Federer, Herbert

Measure and area. (English) Zbl 0046.28402

Bull. Am. Math. Soc. 58, 306-378 (1952).
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Cited in 24 Documents

Keywords:

differentiation and integration
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References:

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[2] A. S. Besicovitch, On surfaces of minimum area, Proc. Cambridge Philos. Soc. 44 (1948), 313 – 334. · Zbl 0038.26401
[3] Lamberto Cesari, Caratterizzazione analitica delle superficie continue di area finita secondo Lebesgue, Ann. Scuola Norm. Super. Pisa (2) 11 (1942), 1 – 42 (Italian). · Zbl 0027.20604
[4] Lamberto Cesari, Sui punti di diramazione delle trasformazioni continue e sull’area delle superficie in forma parametrica, Univ. Roma e Ist. Naz. Alta Mat. Rend. Mat. e Appl. (5) 3 (1942), 37 – 62 (Italian). · Zbl 0026.30901
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[9] Herbert Federer, Surface area. I, Trans. Amer. Math. Soc. 55 (1944), 420 – 437. · Zbl 0060.14003
[10] Herbert Federer, The Gauss-Green theorem, Trans. Amer. Math. Soc. 58 (1945), 44 – 76. · Zbl 0060.14102
[11] Herbert Federer, Coincidence functions and their integrals, Trans. Amer. Math. Soc. 59 (1946), 441 – 466. · Zbl 0060.14101
[12] Herbert Federer, The (\?,\?) rectifiable subsets of \?-space, Trans. Amer. Soc. 62 (1947), 114 – 192. · Zbl 0032.14902
[13] Herbert Federer, Dimension and measure, Trans. Amer. Math. Soc. 62 (1947), 536 – 547. · Zbl 0032.15001
[14] Herbert Federer, Essential multiplicity and Lebesgue area, Proc. Nat. Acad. Sci. U. S. A. 34 (1948), 611 – 616. · Zbl 0032.14903
[15] Herbert Federer, Hausdorff measure and Lebesgue area, Proc. Nat. Acad. Sci. U. S. A. 37 (1951), 90 – 94. · Zbl 0042.28402
[16] Felix Hausdorff, Dimension und äußeres Maß, Math. Ann. 79 (1918), no. 1-2, 157 – 179 (German). · JFM 46.0292.01 · doi:10.1007/BF01457179
[17] Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, v. 4, Princeton University Press, Princeton, N. J., 1941. · Zbl 0060.39808
[18] E. J. McShane, Parametrizations of saddle surfaces, with application to the problem of plateau, Trans. Amer. Math. Soc. 35 (1933), no. 3, 716 – 733. · Zbl 0007.11902
[19] Edward F. Moore, Convexly generated \?-dimensional measures, Proc. Amer. Math. Soc. 2 (1951), 597 – 606. · Zbl 0044.04902
[20] Edward F. Moore, Density ratios and (\?,1) rectifiability in \?-space, Trans. Amer. Math. Soc. 69 (1950), 324 – 334. · Zbl 0040.25003
[21] Anthony P. Morse, A theory of covering and differentiation, Trans. Amer. Math. Soc. 55 (1944), 205 – 235. · Zbl 0063.04111
[22] H. Federer and A. P. Morse, Some properties of measurable functions, Bull. Amer. Math. Soc. 49 (1943), 270 – 277. · Zbl 0063.01319
[23] A. P. Morse and John F. Randolph, The \? rectifiable subsets of the plane, Trans. Amer. Math. Soc. 55 (1944), 236 – 305. · Zbl 0060.14002
[24] Hans Rademacher, Über partielle und totale differenzierbarkeit von Funktionen mehrerer Variabeln und über die Transformation der Doppelintegrale, Math. Ann. 79 (1919), no. 4, 340 – 359 (German). · JFM 47.0243.01 · doi:10.1007/BF01498415
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[26] Tibor Radó, On absolutely continuous transformations in the plane, Duke Math. J. 4 (1938), no. 1, 189 – 221. · Zbl 0019.08801 · doi:10.1215/S0012-7094-38-00415-6
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[28] Tibor Rado, On surface area, Proc. Nat. Acad. Sci. U. S. A. 31 (1945), 102 – 106. · Zbl 0061.10803
[29] Tibor Radó, Length and Area, American Mathematical Society Colloquium Publications, vol. 30, American Mathematical Society, New York, 1948.
[30] Arthur Sard, The equivalence of \?-measure and Lebesgue measure in \?_{\?}, Bull. Amer. Math. Soc. 49 (1943), 758 – 759. · Zbl 0063.06721
[31] Hassler Whitney, On totally differentiable and smooth functions, Pacific J. Math. 1 (1951), 143 – 159. · Zbl 0043.05803
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