The (𝜑,𝑠) regular subsets of 𝑛-space

Marstrand, John M.

doi:10.1090/S0002-9947-1964-0166336-X

The $(\varphi , s)$ regular subsets of $n$-space

Author: John M. Marstrand
Journal: Trans. Amer. Math. Soc. 113 (1964), 369-392
MSC: Primary 28.80
DOI: https://doi.org/10.1090/S0002-9947-1964-0166336-X
MathSciNet review: 0166336
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A. S. Besicovitch, On the fundamental geometrical properties of linearly measurable plane sets of points (II), Math. Ann. 115 (1938), no. 1, 296–329. MR 1513189, DOI https://doi.org/10.1007/BF01448943
Herbert Federer, The $(\varphi ,k)$ rectifiable subsets of $n$-space, Trans. Amer. Math. Soc. 62 (1947), 114–192. MR 22594, DOI https://doi.org/10.1090/S0002-9947-1947-0022594-3
J. M. Marstrand, Circular density of plane sets, J. London Math. Soc. 30 (1955), 238–246. MR 67964, DOI https://doi.org/10.1112/jlms/s1-30.2.238
J. M. Marstrand, Hausdorff two-dimensional measure in $3$-space, Proc. London Math. Soc. (3) 11 (1961), 91–108. MR 123670, DOI https://doi.org/10.1112/plms/s3-11.1.91
Edward F. Moore, Density ratios and $(\phi ,1)$ rectifiability in $n$-space, Trans. Amer. Math. Soc. 69 (1950), 324–334. MR 37894, DOI https://doi.org/10.1090/S0002-9947-1950-0037894-0
Anthony P. Morse, The role of internal families in measure theory, Bull. Amer. Math. Soc. 50 (1944), 723–728. MR 11107, DOI https://doi.org/10.1090/S0002-9904-1944-08223-2
A. P. Morse and John F. Randolph, The $\phi $ rectifiable subsets of the plane, Trans. Amer. Math. Soc. 55 (1944), 236–305. MR 9975, DOI https://doi.org/10.1090/S0002-9947-1944-0009975-6

S. Saks, Theory of the integral, Hafner, Warsaw, 1937; §9, p. 82.