summable function

A measurable functionMathworldPlanetmath f:Ω where (Ω,𝒜,μ) is a measure spaceMathworldPlanetmath is said to be summable if the Lebesgue integralMathworldPlanetmath of the absolute valueMathworldPlanetmathPlanetmathPlanetmath of f exists and is finite,


An alternative way of expressing this condition is to assert that fL1(Ω).

Note that some authors distinguish between integrable and summable: an integrable function is one for which the above integral exists; a summable function is one for which the integral exists and is finite.

Title summable function
Canonical name SummableFunction
Date of creation 2013-03-22 18:12:14
Last modified on 2013-03-22 18:12:14
Owner ehremo (15714)
Last modified by ehremo (15714)
Numerical id 8
Author ehremo (15714)
Entry type Definition
Classification msc 28A25
Related topic LebesgueIntegrable