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

Goffman, Casper; Pedrick, George

doi:10.1090/S0002-9939-1975-0376995-7

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A proof of the homeomorphism of Lebesgue-Stieltjes measure with Lebesgue measure
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by Casper Goffman and George Pedrick PDF

Proc. Amer. Math. Soc. 52 (1975), 196-198 Request permission

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.

References

J. C. Oxtoby and S. M. Ulam, Measure-preserving homeomorphisms and metrical transitivity, Ann. of Math. (2) 42 (1941), 874–920. MR 5803, DOI 10.2307/1968772