ThmDex – An index of mathematical definitions, results, and conjectures.

F11271

Formulation 0

Let $X$ and $Y$ each be a D202: Random variable such that

(i)	$f$ is a D201: Measurable map

Then

(1)	\begin{equation} I(X; Y) \geq I(X; f(Y)) \end{equation}
(2)	\begin{equation} I(X; Y) = I(X; f(Y)) \quad \iff \quad I(X; Y \mid f(Y)) = 0 \end{equation}