Entropy monotonicity under independent addition
= Entropy monotonicity under independent addition
If $U,V$ are <independent random variables> taking values in a countable additive group, conditioning on $V$ makes $U+V$ a translate of $U$. Consequently $H(U+V\mid V)=H(U)$, and <conditional entropy> gives $H(U+V)\geq H(U)$. If the two <information entropies> are finite, equality holds exactly when $U+V$ and $V$ are independent.
// Target: probability-and-statistics.bigb