\begin{definition}[Definition:Integrable Function/Lebesgue]
Let $\lambda^n$ be a Lebesgue measure on $\R^n$ for some $n > 0$.
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, for all real numbers $p \ge 1$, $f$ is said to be '''Lebesgue $p$-integrable''' {{iff}} it is $p$-integrable under $\lambda^n$.
\end{definition}