\begin{definition}[Definition:Lebesgue Integral]
Let $\lambda^n$ be a Lebesgue measure on $\R^n$.
Let $f: \R^n \to \overline \R$ be a Lebesgue integrable function.
Then the $\lambda^n$-integral of $f$:
:$\ds \int f \rd \lambda^n$
is called the '''Lebesgue integral of $f$'''.
\end{definition}