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 $\mu$ :


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

is $\mu$-integrable.

Also see

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