Definition:Integrable Function/Lebesgue

Definition
Let $\lambda^n$ be Lebesgue measure on $\R^n$.

Let $f: \R^n \to \overline{\R}$ be an extended real-valued function.

Then $f$ is said to be Lebesgue integrable iff it is $\lambda^n$-integrable.

Similarly, $f$ is said to be Lebesgue $p$-integrable iff it is $p$-integrable under $\lambda^n$.

Also see

 * Lebesgue Integral