Definition:P-Integrable Function

Definition

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.

Let $p \ge 1$ be a real number.

Then $f$ is said to be $p$-integrable in respect to $\mu$ iff:

$\displaystyle \int \left\vert{f}\right\vert^p \ \mathrm d \mu < +\infty$

is integrable.