Let $A,B \in \mathcal{B}$ two sets, and let $X$ and $Y$ be two independent Gaussian variables with means $\mu_1 ,\mu_2$ and deviations $\sigma_1$ and $\sigma_2$.Now let $Z=X+Y$.
How can I compute $P(Z \in A|X\in B$ )?
Note: I am not sure if the question makes sense. I am trying to prove that Brownian motion satisfies the strong mixing conditions. If you could at least point me to the proof of some similar result, I would be grateful.
