Definition:Join of Finite Partitions

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Definition

Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.

Let $\xi, \eta$ be finite partitions of $\Omega$.

The join of $\xi$ and $\eta$ is the finite partition defined as:

$\ds \xi \vee \eta := \set {A \cap B : A \in \xi, B \in \eta} \setminus \set\O$

Also see

• Properties of Join

Sources

• 2013: Peter Walters: An Introduction to Ergodic Theory (4th ed.) $4.1$: Partitions and Subalgebras