Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From weak to strong types of $L_E^1$-convergence by the Bocce-criterion   Necessary and sufficient oscillation conditions are given for a weakly
convergent sequence (resp. relatively weakly compact set) in the
Bochner-Lebesgue space $\l1$ to be norm convergent (resp. relatively norm
compact), thus extending the known results for $\rl1$. Similarly, necessary and
sufficient oscillation conditions are given to pass from weak to limited (and
also to Pettis-norm) convergence in $\l1$. It is shown that tightness is a
necessary and sufficient condition to pass from limited to strong convergence.
Other implications between several modes of convergence in $\l1$ are also
studied.

17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics