A proof of Cauchy's theorem (Q2565349)

Using a standard subdivision argument, the authors prove the following homology version of Cauchy's theorem: if \(G\) is an open subset of the complex plane, \(f\) is an analytic function on \(G\) and \(\beta\) is a 1-chain on \(G\) which is the boundary of a 2-chain so that each summand of \(\partial\beta\) is rectifiable then \(\int_\beta f=0\).