Measure Space

Definition

A measure space is a measurable space with a measure corresponding to the given sigma-algebra.

Explicitly, given a set \(X\) with a \(\sigma\)-algebra \(\mathcal{F}\) and measure \(\mu : \mathcal{F} \to [0, \infty]\), the triple

\[ (X, \mathcal{F}, \mu)\]

is a measure space.