ThmDex – An index of mathematical definitions, results, and conjectures.
Formulation F3871 on D1697: Sigma-bounded measure
F3871
Formulation 0
Let $M = (X, \mathcal{F})$ be a D1108: Measurable space.
A D85: Unsigned basic measure $\mu : \mathcal{F} \to [0, \infty]$ is a sigma-bounded measure on $M$ if and only if there exists $E_0, E_1, E_2, \dots \in \mathcal{F}$ such that
(1) $X = \bigcup_{n \in \mathbb{N}} E_n$ (D74: Set cover)
(2) $\forall \, n \in \mathbb{N} : \mu(E_n) < \infty$