The Nonparametric Weierstrass Integral over a BV Curve as a Length Functional

This paper pursues the aim of finding geometrical characterizations for the nonparametric Weierstrass integral. I prove that, under quite natural conditions, the nonparametric Weierstrass integral is a length functional with regard to a suitable metric. An analogous result was proved in L. Faina Studia Math 127 1998., 9]19.for the parametric case.