Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On variational principles for metric mean dimension   In this note, we show several variational principles for metric mean
dimension. First we prove a variational principles in terms of Shapira's
entropy related to finite open covers. Second we establish a variational
principle in terms of Katok's entropy. Finally using these two variational
principles we develop a variational principle in terms of Brin-Katok local
entropy.

17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex