# Conditional expectation

How can I do this?

Let X,Y r.v., $$\mathbb{E}(X|Y)=Y$$ and $$\mathbb{E}(Y|X)=X$$.
Proove that X=Y a.s.

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Let X,Y r.v., $$\mathbb{E}(X|Y)=Y$$ and $$\mathbb{E}(Y|X)=X$$.
could you give the definition of $$\mathbb{E}(X|Y)$$ then it might be easier