X,Y,Z are random variables of course. I have seen that this is considered equal sometimes but I need confirmation.
I tried using H(A,B) = H(A|B) + H(B):
H(X | (Y,Z)) = H(X,Y,Z) - H(Y,Z)
and
H(Y,Z) = H(Y|Z) + H(Z)
so
H(X | (Y,Z)) = H(X,Y,Z) - H(Y|Z) - H(Z) = H((X,Y)|Z) - H(Y|Z).
If one assumes that H((X,Y)|Z) = H(X,(Y|Z)), this implies
H((X,Y)|Z) - H(Y|Z) = H(X,(Y|Z)) - H(Y|Z) = H(X | (Y|Z)).
If one then assumes that H(X | (Y|Z)) = H((X | Y)|Z), one has the desired result.
The problem is that I don't see why one could assume this.
