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arXiv · 1506.01234

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

Andrea Marchese
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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.

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Andrea Marchese. 2015-06-03. Residually many BV homeomorphisms map a null set onto a set of full measure. https://arxiv.org/abs/1506.01234

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