summable function

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

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

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.