for , with equality if
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 -additivity. A finitely additive measure has the same definition except that 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.
Lebesgue measure on is one important example of a measure.
|Date of creation||2013-03-22 11:57:33|
|Last modified on||2013-03-22 11:57:33|
|Last modified by||djao (24)|