Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Lebesgue measure of sum-level sets for continued fractions   In this paper we give a detailed measure theoretical analysis of what we call
sum-level sets for regular continued fraction expansions. The first main result
is to settle a recent conjecture of Fiala and Kleban, which asserts that the
Lebesgue measure of these level sets decays to zero, for the level tending to
infinity. The second and third main result then give precise asymptotic
estimates for this decay. The proofs of these results are based on recent
progress in infinite ergodic theory, and in particular, they give non-trivial
applications of this theory to number theory. The paper closes with a
discussion of the thermodynamical significance of the obtained results, and
with some applications of these to metrical Diophantine analysis.

17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int