A measurable function $f : \Omega \to \reals$ 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, \begin{equation*} \int_{\Omega} |f| d\mu < +\infty \end{equation*}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.