A proof of the homeomorphism of Lebesgue-Stieltjes measure with Lebesgue measure
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- by Casper Goffman and George Pedrick
- Proc. Amer. Math. Soc. 52 (1975), 196-198
- DOI: https://doi.org/10.1090/S0002-9939-1975-0376995-7
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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.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
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 52 (1975), 196-198
- MSC: Primary 28A05; Secondary 28A60
- DOI: https://doi.org/10.1090/S0002-9939-1975-0376995-7
- MathSciNet review: 0376995