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 .