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MiS Preprint
34/2015

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

Andrea Marchese

Abstract

Let $Q=[0,1]^2$ be the unit square in $\mathbb{R}^2$. We prove that in a suitable complete metric space of $BV$ homeomorphisms $f:Q\rightarrow Q$ with $f_{|\partial Q}=Id$, the generical homeomorphism (in the sense of Baire categories) maps a null set in a set of full measure and vice versa. Moreover we observe that, for $1\leq p<2$, in the most reasonable complete metric space for such problem, the family of $W^{1,p}$ homemomorphisms satisfying the above property is of first category, instead.

Received:
Jun 3, 2015
Published:
Jun 4, 2015
MSC Codes:
46B35, 26B35
Keywords:
Sobolev homeomorphism, baire categories, piecewise affine homeomorphism

Related publications

inJournal
2019 Repository Open Access
Andrea Marchese

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

In: Proceedings of the Royal Society of Edinburgh / A, 149 (2019) 4, pp. 1047-1059