MathGloss

A measure $\mu$ on a measurable space $(X,\mathcal M)$ is a function $\mu:\mathcal M \to [0,\infty]$ valued on the extended real numbers for which $\mu(\emptyset) = 0$ for any countable, pairwise disjoint collection ${E_i}_{i\in\mathbb N}$ of measurable sets, $$\mu\left(\bigcup_{i\in\mathbb N} E_i\right) = \sum_{i\in\mathbb N} \mu(E_i).$$

A measure space is a measurable space $(X,\mathcal M)$ together with a measure $\mu$ on $\mathcal M$.

Wikidata ID: Q3058212

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