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.

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.

Also see

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