Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximate Carath{\'e}odory's theorem in uniformly smooth Banach spaces   We study the 'no-dimension' analogue of Carath{\'e}odory's theorem in Banach
spaces. We prove such a result together with its colorful version for uniformly
smooth Banach spaces. It follows that uniform smoothness leads to a greedy
de-randomization of Maurey's classical lemma \cite{pisier1980remarques}, which
is itself a 'no-dimension' analogue of Carath{\'e}odory's theorem with a
probabilistic proof. We find the asymptotically tight upper bound on the
deviation of the convex hull from the $k$-convex hull of a bounded set in $L_p$
with $1 < p \leq 2$ and get asymptotically the same bound as in Maurey's lemma
for $L_p$ with $1 < p < \infty.$

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The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an