Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Interval-type theorems concerning means   Each family $\mathcal{M}$ of means has a natural, partial order (point-wise
order), that is $M \le N$ iff $M(x) \le N(x)$ for all admissible $x$.
  In this setting we can introduce the notion of interval-type set (a subset
$\mathcal{I} \subset \mathcal{M}$ such that whenever $M \le P \le N$ for some
$M,\,N \in \mathcal{I}$ and $P \in \mathcal{M}$ then $P \in \mathcal{I}$). For
example, in the case of power means there exists a natural isomorphism between
interval-type sets and intervals contained in real numbers. Nevertheless there
appear a number of interesting objects for a families which cannot be linearly
ordered.
  In the present paper we consider this property for Gini means and Hardy
means. Moreover some results concerning $L^\infty$ metric among (abstract)
means will be obtained.

3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat