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Revision difference : summable function
Version 4 Version 3
A measurable function $f : \Omega \to \reals$ where $(\Omega, \mathcal{A}, \mu)$ is a measure space is said to be {\bf summable} or {\bf integrable} if the Lebesgue integral of the absolute value of $f$ exists and is finite, A measurable function $f : \Omega \to \reals$ where $(\Omega, \mathcal{A}, \mu)$ is a measure space is said to be {\bf summable} or {\bf integrable} if the Lebesgue integral of the absolute value of $f$ exists and is finite,
\begin{equation*} \begin{equation*}
\int_{\Omega} |f| d\mu < +\infty \int_{\Omega} |f| d\mu < +\infty
\end{equation*} \end{equation*}
An alternative way of expressing this condition is to assert that $f \in L^1(\Omega)$. An alternative way of expressing this condition is to assert that $f \in L^1(\Omega)$.