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
Full-text PDF Free Access
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.
J. C. Oxtoby and S. M. Ulam, Measure-preserving homeomorphisms and metrical transitivity, Ann. of Math. (2) 42 (1941), 874-920. MR 3, 211.