# On Cauchy’s Integral Theorem in the Real Plane

• Karl Menger
Chapter

## Abstract

In a rectangle R let p (x, y) and q (x, y) be two continuous functions, and associate with each rectifiable curve C the number $$J(C) = {{\smallint }_{c}}pdx + qdy$$. Under which conditions is J the same for any two coterminal curves in R?