ABSTRACT
P roof. (3) implies A g(I) = f f σ for every cell 1 in K. That is, Ag = S where S is the additive summant in Theorem 3 (§1.6) defined by S(I) = f f σ for every cell I in K . So dg = [S'] = σ by Theorem 3 (§1.6). □
Theorem 1 supports the standard technique for evaluating integrals. Given an integrable differential σ on a cell K find a function g on K such that dg = σ. Then compute Ag{K) to evaluate JK σ.
