Measurability of the Banach indicatrix
Volume 153 / 2018
Colloquium Mathematicum 153 (2018), 97-101
MSC: Primary 28A20; Secondary 28A05.
DOI: 10.4064/cm6881-7-2017
Published online: 16 April 2018
Abstract
We establish the measurability of the Banach indicatrix for a measurable mapping in a geometrically doubling metric space. This is a generalization of a known result for continuous transformations in Euclidean space. A system of dyadic cubes in metric space is employed to construct a sequence of measurable functions converging to the indicatrix, and we partly follow Banach’s original proof.
