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 with respect to $\mu$ if and only if:

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

is $\mu$-integrable.

Also see

• Definition:Measure-Integrable Function
• Definition:Integral of Measure-Integrable Function, justifying the name integrable function
• Definition:Space of Integrable Functions