Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A CAT(0)-valued pointwise ergodic theorem   In this note we prove the a pointwise ergodic theorem for functions taking
values in a separable complete CAT(0)-space, analogous to Lindenstrauss'
pointwise ergodic theorem for real-valued integrable functions on a probability
space subject to a probability-preserving action of an amenable l.c.s.c. group,
where in the CAT(0) setting the role of ergodic averages is played by the
barycentres of the empirical distributions of a CAT(0)-valued map along an
orbit of the group action. The proof rests on an approximation argument and an
appeal to that result for real-valued maps.

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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat