Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Hoffmann-Jorgensen inequality in metric semigroups   We prove a refinement of the inequality by Hoffmann-Jorgensen that is
significant for three reasons. First, our result improves on the
state-of-the-art even for real-valued random variables. Second, the result
unifies several versions in the Banach space literature, including those by
Johnson and Schechtman [Ann. Probab. 17 (1989)], Klass and Nowicki [Ann.
Probab. 28 (2000)], and Hitczenko and Montgomery-Smith [Ann. Probab. 29
(2001)]. Finally, we show that the Hoffmann-Jorgensen inequality (including our
generalized version) holds not only in Banach spaces but more generally, in a
very primitive mathematical framework required to state the inequality: a
metric semigroup $\mathscr{G}$. This includes normed linear spaces as well as
all compact, discrete, or (connected) abelian Lie groups.

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The categories of this paper are: cs
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th