Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A descriptive set theorist's proof of the pointwise ergodic theorem   We give a short combinatorial proof of the classical pointwise ergodic
theorem for probability measure preserving $\mathbb{Z}$-actions. Our approach
reduces the theorem to a tiling problem: tightly tile each orbit by intervals
with desired averages. This tiling problem is easy to solve for $\mathbb{Z}$
with intervals as tiles. However, it would be interesting to find other classes
of groups and sequences of tiles for which this can be done, since then our
approach would yield a pointwise ergodic theorem for such classes.

27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th