Definition:Finite Partition (Probability Theory)
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Definition
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.
Let $\xi$ be a partition of $\Omega$.
Then, $\xi$ said to be a finite partition if and only if:
- $\exists A_1, \ldots, A_n \in \Sigma : \xi = \set {A_1, \ldots, A_n}$
Also see
- Definition:Finite Partition Generated by Finite Sub-Sigma-Algebra
- Sigma-Algebra Generated by Finite Partition is Finite Sub-Sigma-Algebra
Sources
- 2013: Peter Walters: An Introduction to Ergodic Theory (4th ed.) $4.1$: Partitions and Subalgebras