ThmDex – An index of mathematical definitions, results, and conjectures.
Formulation F11268 on R3503: Data processing inequality
F11268
Formulation 0
Let $X$, $Y$, and $Z$ each be a D202: Random variable such that
(i) $X \to Y \to Z$ is a D3348: Markov chain
Then
(1) \begin{equation} I(X; Y) \geq I(X; Z) \end{equation}
(2) \begin{equation} I(X; Y) = I(X; Z) \quad \iff \quad I(X; Y \mid Z) = 0 \end{equation}