Definition:Integrable Function/p-Integrable

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.

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


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

is integrable.

Also see

 * Integrable Function
 * Integral of Integrable Function, justifying the name integrable function
 * Space of Integrable Functions