Definition:Entropy of Finite Sub-Sigma-Algebra
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Definition
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.
Let $\AA \subseteq \Sigma$ be a finite sub-$\sigma$-algebra.
The entropy of $\AA$ is defined as:
- $\ds \map H \AA := \map H {\map \xi \AA}$
where:
- $\map \xi \AA$ is the finite partition generated by $\AA$
- $\map H \cdot$ on the right hand side denotes the entropy of finite partition
Also see
Sources
- 2013: Peter Walters: An Introduction to Ergodic Theory (4th ed.) $4.2$: Entropy of a Partition