ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
▼ Deduction system
▼ Theory
▼ Zermelo-Fraenkel set theory
▼ Set
▼ Subset
▼ Power set
▼ Hyperpower set sequence
▼ Hyperpower set
▼ Hypersubset
▼ Subset algebra
▼ Boolean algebra
▼ Sigma-algebra
▼ Discrete sigma-algebra
▼ Discrete measurable space
▼ Point-mass measure
Definition D1225
Counting measure
Formulation 0
Let $M = (X, \mathcal{F})$ be a D1108: Measurable space such that
(i) $F \subseteq X$ is a D78: Subset of $X$
The counting measure on $M$ with respect to $F$ is the D4361: Unsigned basic function \begin{equation} \mathcal{F} \to [0, \infty], \quad E \mapsto |E \cap F| \end{equation}
Children
▶ D1703: Point measure
▶ D4105: Standard counting measure