Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a class of random sets of positive integers   In this note, we study a class of random subsets of positive integers induced
by Bernoulli random variables. We obtain sufficient conditions such that the
random set is almost surely lacunary, does not have bounded gaps and contains
infinitely many arithmetic progressions, respectively.

14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph