Integration in ℝN
In order to construct the theory of Riemann integration in ℝ N , we need to develop first a theory of volume for sets of points in ℝ N . This development is a straightforward generalization of the theory of area (Jordan content) given in Section 5.4. We shall outline the main steps of the theory and leave the proofs of the theorems to the reader. We recall the definitions of open and closed cells given earlier in Section 6.3.
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