The existence of a measure-preserving bijection from a unit square to a unit segment
Probability
2016-02-03 v1
Abstract
In this paper, we prove the existence of a measure-preserving bijection from unit square to unit segment. This bijection is also called the probability isomorphism between two probability spaces. Then we give a new proof of the existence of the independent random variables on Borel probability space that their distribution functions are the given distribution functions.
Keywords
Cite
@article{arxiv.1602.00800,
title = {The existence of a measure-preserving bijection from a unit square to a unit segment},
author = {Cong Dan Pham},
journal= {arXiv preprint arXiv:1602.00800},
year = {2016}
}