Definition:Integrable Function/p-Integrable

Definition

Let $\struct {X, \Sigma, \mu}$ be a measure space.

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

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

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

$\displaystyle \int \size f^p \rd \mu < +\infty$