Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: ON a certain class of norms in semimodular spaces and their monotonicity
  properties   Let X be a linear space over K, K=R or K=C and let for n>1 \rho_i be s-convex
semimodular defined on X for any i\in{1,...,n-1}. Put \rho=\max_{1\leq i \leq
n-1}\{\rho_i\} and
  X_{\rho}= { x \in X: \rho(dx) < \infty for some d > 0 }. In this paper we
define a new class of s-norms (norms if s=1) on X_{\rho}. In particular, our
defintion generalizes in a natural way the Orlicz-Amemiya and Luxemburg norms
defined for s-convex semimodulars. Then, we investigate order continuous, the
Fatou Property and various monotonicity properties of semimodular spaces
equipped with these s-norms.

16
The categories of this paper are: stat
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an