Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Radial continuous rotation invariant valuations on star bodies   We characterize the positive radial continuous and rotation invariant
valuations $V$ defined on the star bodies of $\mathbb R^n$ as the applications
on star bodies which admit an integral representation with respect to the
Lebesgue measure. That is, $$V(K)=\int_{S^{n-1}}\theta(\rho_K)dm,$$ where
$\theta$ is a positive continuous function, $\rho_K$ is the radial function
associated to $K$ and $m$ is the Lebesgue measure on $S^{n-1}$. As a corollary,
we obtain that every such valuation can be uniformly approximated on bounded
sets by a linear combination of dual quermassintegrals.

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The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga