Conditional Entropy of Join as Sum/Corollary 5

Corollary 5 to Conditional Entropy of Join as Sum
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.

Let $\AA, \DD \subseteq \Sigma$ be finite sub-$\sigma$-algebras.

Then:
 * $\ds \map H \AA \ge \map H {\AA \mid \DD} $

where:
 * $\map H \cdot$ denotes the entropy
 * $\map H {\cdot \mid \cdot}$ denotes the conditional entropy