The parametric Weierstrass integral over a BV curve as a length functional
Volume 127 / 1998
Studia Mathematica 127 (1998), 9-19
DOI: 10.4064/sm-127-1-9-19
Abstract
The constructive definition of the Weierstrass integral through only one limit process over finite sums is often preferable to the more sophisticated definition of the Serrin integral, especially for approximation purposes. By proving that the Weierstrass integral over a BV curve is a length functional with respect to a suitable metric, we discover a further natural reason for studying the Weierstrass integral. This characterization was conjectured by Menger.
