Let $R ⊂ R^N$ be a rectangle and let P = {R1,...,Rn} be a partition of R. Prove that the elementary measure of R is given by the sum of the elementary measure of the rectangles Ri.
So I am trying to use induction on N and am thinking about jordan measure s.t. he measure of an elementary set is composed of a finite number of nonoverlapping rectangles but i have trouble thinking about how to write out the solution rigorously (i thought it would be trivial.)