Let $(X, \mathcal{B}, \mu)$ be a probability space. If $\xi = \{A_1, ..., A_k\}$ is a finite partition of $X$, then the measure theoretic entropy is defined as $$H_\mu(\xi) = -\sum_{i=1}^k \mu(A_i) \; log \; \mu(A_i).$$
How do we define the entropy for an infinite partition? For example, for $\xi = \{ \{x\} : x \in X \}$?