Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entropy and Its Variational Principle for Product Type Dynamical Systems   This paper has a flaw in an argument that uses the weak-* convergence of
measures. The paper was replaced by "Entropy and Its Variational Principle for
Locally Compact Metrizable Systems", by the same authors.

4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an