Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Almost uniform and strong convergences in ergodic theorems for symmetric
  spaces   Let $(\Omega,\mu)$ be a $\sigma$-finite measure space, and let $X\subset
L^1(\Omega)+L^\infty(\Omega)$ be a fully symmetric space of measurable
functions on $(\Omega,\mu)$. If $\mu(\Omega)=\infty$, necessary and sufficient
conditions are given for almost uniform convergence in $X$ (in Egorov's sense)
of Ces\`aro averages $M_n(T)(f)=\frac1n\sum_{k = 0}^{n-1}T^k(f)$ for all
Dunford-Schwartz operators $T$ in $L^1(\Omega)+ L^\infty(\Omega)$ and any $f\in
X$. Besides, it is proved that the averages $M_n(T)$ converge strongly in $X$
for each Dunford-Schwartz operator $T$ in $L^1(\Omega)+L^\infty(\Omega)$ if and
only if $X$ has order continuous norm and $L^1(\Omega)$ is not contained in
$X$.

35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg