I read in a book that gave without proof that if I have that $X,Y,Z$ are jointly independent, then $X \perp cYZ$, where $\perp$ means independent of and $c$ is a finite constant. How can I show this fact from a measure theoretic or even simpler way? thanks!
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1Show that $\sigma(X)$ and $\sigma(Y,Z)$ are independent, where $\sigma(X)$ denotes sigma algebra generated by $X$ – user160738 Dec 12 '15 at 04:31
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1@user160738 Good job finding my question :)) – BCLC Dec 12 '15 at 15:05