Measure, Integration & Real Analysis · Problem 12.12

Probability Measures — Sheldon Axler

Mathematics — Measure Theory · probability-distribution-same-distribution

Problem

Suppose

(\Omega, \mathcal{F}, P)

and

(\Omega', \mathcal{F}', P')

are probability spaces,

X

is a random variable on

\Omega

Y

is a random variable on

\Omega'

, and

\widetilde{X} = \widetilde{Y}

. Prove that

P_X = P'_Y