Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strict $K$-monotonicity and $K$-order continuity in symmetric spaces   This paper is devoted to strict $K$- monotonicity and $K$-order continuity in
symmetric spaces. Using the local approach to the geometric structure in a
symmetric space $E$ we investigate a connection between strict $K$-monotonicity
and global convergence in measure of a sequence of the maximal functions. Next,
we solve an essential problem whether an existence of a point of $K$-order
continuity in a symmetric space $E$ on $[0,\infty)$ implies that the embedding
$E\hookrightarrow{L^1}[0,\infty)$ does not hold. We finish this article with a
complete characterization of $K$-order continuity in a symmetric space $E$ that
is written using a notion of order continuity under some assumptions on the
fundamental function of $E$.

11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th