measure (original) (raw)

Occasionally, the term positive measure is used to distinguish measures as defined here from more general notions of measure which are not necessarily restricted to the non-negative extended reals.

The second property above is called countable additivity, or σ-additivity. A finitely additive measure μ has the same definition except that ℬ⁢(E) is only required to be an algebra and the second property above is only required to hold for finite unions. Note the slight abuse of terminology: a finitely additive measure is not necessarily a measure.