Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counter-examples to the Dunford-Schwartz pointwise ergodic theorem on
  $L^1+L^\infty$   Extending a result by Chilin and Litvinov, we show by construction that given
any $\sigma$-finite infinite measure space $(\Omega,\mathcal{A}, \mu)$ and a
function $f\in L^1(\Omega)+L^\infty(\Omega)$ with
$\mu(\{|f|>\varepsilon\})=\infty$ for some $\varepsilon>0$, there exists a
Dunford-Schwartz operator $T$ over $(\Omega,\mathcal{A}, \mu)$ such that
$\frac{1}{N}\sum_{n=1}^N (T^nf)(x)$ fails to converge for almost every
$x\in\Omega$. In addition, for each operator we construct, the set of functions
for which pointwise convergence fails almost everywhere is residual in
$L^1(\Omega)+L^\infty(\Omega)$.

26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex