In mathematics, specifically measure theory, the counting measure is an intuitive way to put a measure on any set – the "size" of a subset is taken to be the number of elements in the subset if the subset has finitely many elements, and \infty if the subset is infinite.

The counting measure can be defined on any measurable space along with a sigma-algebra) but is mostly used on countable sets.

into a measurable space by taking the power set as the sigma-algebra denotes the cardinality

is σ-finite is countable.

Integration on the set of natural numbers with counting measure

Discussion

where the possibly uncountable sum of real numbers is defined to be the supremum gives the counting measure.

See also

References