Category:Integrable Functions

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This category contains results about Integrable Functions.

Let $\left({X, \Sigma, \mu}\right)$ be a measure space.

Let $f \in \mathcal{M}_{\overline{\R}}, f: X \to \overline{\R}$ be a measurable function.

Then $f$ is said to be $\mu$-integrable if and only if:

$\displaystyle \int f^+ \, \mathrm d\mu < +\infty$


$\displaystyle \int f^- \, \mathrm d\mu < +\infty$

where $f^+$, $f^-$ are the positive and negative parts of $f$, respectively.