(i) | $X : \Omega \to \mathcal{X}$ and $Y : \Omega \to \mathcal{Y}$ are each a D5723: Simple random variable on $P$ |
The joint entropy of $(X, Y)$ in base $a$ is the D4767: Unsigned real number \begin{equation} - \sum_{x \in \mathcal{X}} \sum_{y \in \mathcal{Y}} \mathbb{P}(X = x, Y = y) \log_a \mathbb{P}(X = x, Y = y) \end{equation}