Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Residually many BV homeomorphisms map a null set onto a set of full
  measure   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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The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga