Hi

A little question...

Let $\displaystyle \Omega$ be the probability space.

We know that if $\displaystyle P(A)=1$, then $\displaystyle P(\Omega \backslash A)=0$ (we don't necessarily have $\displaystyle A=\Omega$)

Is there a proof (with formulae, not diagrams) for that :

For any $\displaystyle X \subset \Omega$, if P(A)=1, then $\displaystyle P(A \cap X)=P(X)$

?

Thanks