# conditional entropy of function

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• May 3rd 2012, 04:08 PM
alexandrabel90
conditional entropy of function
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?
• May 3rd 2012, 04:33 PM
jens
Re: conditional entropy of function
$f(X)$ is a degraded observation of $X$, so we have that

$H(Y|f(X),X) = H(Y|X)$

Since conditioning reduces entropy,

$H(Y|f(X)) \geq H(Y|X)$