ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
▼ Deduction system
▼ Theory
▼ Zermelo-Fraenkel set theory
▼ Set
▼ Binary cartesian set product
▼ Binary relation
▼ Map
▼ Operation
▼ N-operation
▼ Binary operation
▼ Enclosed binary operation
▼ Groupoid
▼ Ringoid
▼ Semiring
▼ Ring
▼ Left ring action
▼ Module
▼ Vector space
▼ Vector space seminorm
▼ Vector space norm
▼ Normed vector space
▼ Bounded set
▼ Bounded map
▼ Constant-bounded map
▼ Constant-bounded function
▼ Finite measure
Definition D1697
Sigma-bounded measure
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) $\forall \, n \in \mathbb{N} : \mu(E_n) < \infty$