The nonparametric Weierstrass integral over a BV curve as a length functional (Q1973947)

Following the outline of Menger's conjecture [\textit{K. Menger}, ``Géométrie générale'', Mém. Sci. Math. (1954; Zbl 0055.16001)] the author proves that the nonparametric Weierstrass integral over a BV curve [\textit{P. Brandi} and \textit{A. Salvadori}, ``On the definition and properties of a variational integral over a BV curve'', Rapporto Tecnico Dip. Math. Univ. Perugia (1988), ``On the non-parametric integral over a BV surface'', Nonlinear Anal., Theory Methods Appl. 13, 1127-1137 (1989; Zbl 0694.49029)] is a length with respect to a suitable metric. The parametric case was considered by the same author in ``The parametric Weierstrass integral over a BV curve as a length functional'' [Stud. Math. 127, 9-19 (1998; Zbl 0906.49020)].