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Residually many BV homeomorphisms map a null set onto a set of full measure

Published online by Cambridge University Press:  27 December 2018

Andrea Marchese*
Affiliation:
Institut für Mathematik, Mathematisch-naturwissenschaftliche Fakultät, Universität Zürich Winterthurerstrasse 190, Zürich CH-8057, Switzerland ([email protected])

Abstract

Let Q be the open unit square in ℝ2. We prove that in a natural complete metric space of BV homeomorphisms f : QQ with f|∂Q = Id, residually many homeomorphisms (in the sense of Baire categories) map a null set onto a set of full measure, and vice versa. Moreover, we observe that for 1 ⩽ p < 2, the family of W1,p homemomorphisms satisfying the above property is of the first category.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2018 

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