Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariant measures and measurable projective factors for actions of
  higher-rank lattices on manifolds   We consider smooth actions of lattices in higher-rank semisimple Lie groups
on manifolds. We define two numbers $r(G)$ and $m(G)$ associated with the roots
system of the Lie algebra of a Lie group $G$. If the dimension of the manifold
is smaller than $r(G)$, then we show the action preserves a Borel probability
measure. If the dimension of the manifold is at most $m(G)$, we show there is a
quasi-invariant measure on the manifold such that the action is measurable
isomorphic to a relatively measure preserving action over a standard boundary
action.

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The categories of this paper are: funct-an
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con