A Proof of the Homeomorphism of Lebesgue-Stieltjes Measure with Lebesgue Measure
Casper Goffman, George Pedrick · Proceedings of the American Mathematical Society · 1975
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.