Let be a closed Jordan domain and a bounded function. We adopt the convention that is extended to by .

Let be a finite set of Jordan domains in that cover .

Define ,

(upper R-sum)

(lower R-sum)

Define , .

Say that is -integrable on if .

**Prove** that if is Riemann integrable on then it is -integrable.

How to relate this? The definition of Riemann integrable has only a difference that is an n-dimensional rectangle and is a grid on .