Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Volume, Polar Volume and Euler Characteristic for Convex Functions   Functional analogs of the Euler characteristic and volume together with a new
analog of the polar volume are characterized as non-negative, continuous,
$\operatorname{SL}(n)$ and translation invariant valuations on the space of
finite, convex and coercive functions on ${\mathbb R}^n$.

28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph