# Existence of measure factorization

Let $(\Omega,\mathcal F,\mathbb P)$ a probability space, $(X,\mathcal B)$ a measurable space and $m$ a probability measure on $\Omega\times X$ such that its projection on $\Omega$ is equal to $\mathbb P$.

When $m$ has a factorization with respect to $\mathbb P$?

-
What is $(X, \mathcal{B})$ for? I think $m$ is defined over $(\Omega, \mathcal{P})$... –  André Caldas Nov 29 '11 at 16:37
Can you double-check your notation, and explain what you mean by "factorization"? –  Nate Eldredge Nov 29 '11 at 16:40
I guess paul wants to determine whether there exists a measure $\mu$ such that $m=\mathcal P\otimes \mu$. –  Davide Giraudo Nov 3 '12 at 15:37