Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Brezis-Lieb Lemma without pointwise convergence   Brezis-Lieb lemma is a refinement of Fatou lemma providing an evaluation of
the gap between the integral for a sequence and the integral for its pointwise
limit. This note studies the question if such gap can be evaluated when there
is no a.e. convergence. In particular, it gives the same lower bound for the
gap in L^p as the gap in the Brezis-Lieb lemma (including the case
vector-valued functions) provided that p is greater or equal than 3 and the
sequence converges both weakly and weakly in the sense of a duality map. It
also shows that the statement is false if p<3. An application is given in form
of a Brezis-Lieb lemma for gradients.

19
The categories of this paper are: eess
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci