I am trying to learn free probability from scratch, mostly by myself. I am trying to prove the following result.
If $\mu$ and $\nu$ are compactly supported probability measures, then there exists a $C^*$ probability space $(\mathcal{A}, \phi)$ and self adjoint $a,~b\in \mathcal{A}$ which are free independent and have distributions $\mu$ and $\nu$ respectively.
I was told that this can be easily proved using free products of $*$-probability spaces. But I can not see how it follows. Can someone give me a line of proof, or point out some place where I can get the result? Advanced thanks for any helps/suggestions.