Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Baire measurable paradoxical decompositions via matchings   We show that every locally finite bipartite Borel graph satisfying a
strengthening of Hall's condition has a Borel perfect matching on some comeager
invariant Borel set. We apply this to show that if a group acting by Borel
automorphisms on a Polish space has a paradoxical decomposition, then it admits
a paradoxical decomposition using pieces having the Baire property. This
strengthens a theorem of Dougherty and Foreman who showed that there is a
paradoxical decomposition of the unit ball in $\mathbb{R}^3$ using Baire
measurable pieces. We also obtain a Baire category solution to the dynamical
von Neumann-Day problem: if $a$ is a nonamenable action of a group on a Polish
space $X$ by Borel automorphisms, then there is a free Baire measurable action
of $\mathbb{F}_2$ on $X$ which is Lipschitz with respect to $a$.

7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph