how does one show that H(Y l f(X) ) greater than or equal to H(YlX) where f(X) is any function of X?
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$\displaystyle f(X)$ is a degraded observation of $\displaystyle X$, so we have that $\displaystyle H(Y|f(X),X) = H(Y|X)$ Since conditioning reduces entropy, $\displaystyle H(Y|f(X)) \geq H(Y|X)$
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