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Title

The parametric Weierstrass integral over a BV curve as a length functional

Authors 1

Affiliations

  1. Dipartimento di Matematica, Università di Perugia, Via L. Vanvitelli, 1, 06123 Perugia, Italy

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.

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Studia Mathematica
1998/127/1
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Pages:
9-19
Main language of publication
English
Received
1996-05-06
Accepted
1997-06-17
Published
1998
Exact and natural sciences