English

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 ([0,1],\B([0,1]),\Lb)([0,1],\B([0,1]),\Lb) 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}
}