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A proof of the homeomorphism of Lebesgue-Stieltjes measure with Lebesgue measure

Authors: Casper Goffman and George Pedrick
Journal: Proc. Amer. Math. Soc. 52 (1975), 196-198
MSC: Primary 28A05; Secondary 28A60
MathSciNet review: 0376995
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Abstract: An elementary proof is given of the fact that nonatomic measures on $ n$ space, for which open sets have positive measure, are ``homeomorphic". The proof is based on the fact that for such measures all hyperplanes in most directions have measure zero.

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  • [1] J. C. Oxtoby and S. M. Ulam, Measure-preserving homeomorphisms and metrical transitivity, Ann. of Math. (2) 42 (1941), 874-920. MR 3, 211. MR 0005803 (3:211b)

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