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) $\forall \, n \in \mathbb{N} : \mu(E_n) < \infty$