Category:Counting Measure

This category contains results about Counting Measure.

Let $\struct {X, \Sigma}$ be a measurable space.

The counting measure (on $X$), denoted $\size {\, \cdot \,}$, is the measure defined by:

$\size {\, \cdot \,}: \Sigma \to \overline \R, \ \size E := \begin {cases} \map \# E & : \text {$E$ is finite} \\ +\infty & : \text {$E$ is infinite} \end{cases}$

where $\overline \R$ denotes the extended real numbers, and $\#$ denotes cardinality.