If we have two random variables $X$ and $Y$ is the following relation true:
$\int g(X,Y) ~~ dP = \int g(x,y) ~~dF_{X,Y}$
2026-03-26 02:26:41.1774492001
Function of two random variables
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Yes, if by $F_{X,Y}$ you mean $F_{X,Y}(A\times B):=P[X\in A,Y\in B]$ (along with appropriate conditions on the rest of the notation). You can prove it like in this post.