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How can be proven that for random variables $A$ and $B$, and $C = A + B$,

$$H(C\mid A) = H(B\mid A).$$

Also, would it be possible to determine if $H(C)$ would be greater than $H(A)$?

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    Differential or Shannon entropy, or some other type of entropy?2018-02-03
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    Seems roughly equivalent to showing $H(A,A+B)=H(A,B)$.2018-02-03
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    Is the fact that the operation is addition important? Should this statement also hold: $H(A,AB)=H(A,B)$, under suitable conditions? Or could it more generally be $H(A,f(A,B))=H(A,B)$?2018-02-03

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