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} |