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