# summable function

A measurable function $f:\Omega\to\mathbb{R}$ where $(\Omega,\mathcal{A},\mu)$ is a measure space is said to be summable if the Lebesgue integral of the absolute value of $f$ exists and is finite,

 $\int_{\Omega}|f|d\mu<+\infty$

An alternative way of expressing this condition is to assert that $f\in L^{1}(\Omega)$.

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 SummableFunction 2013-03-22 18:12:14 2013-03-22 18:12:14 ehremo (15714) ehremo (15714) 8 ehremo (15714) Definition msc 28A25 LebesgueIntegrable