Proving X=Y with Conditional Expectation

[yavanna]

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.

 

[bpet]

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.

could you give the definition of $$\mathbb{E}(X|Y)$$ then it might be easier