Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On metric characterizations of the Radon-Nikod\'ym and related
  properties of Banach spaces   We find a class of metric structures which do not admit bilipschitz
embeddings into Banach spaces with the Radon-Nikod\'ym property. Our proof
relies on Chatterji's (1968) martingale characterization of the RNP and does
not use the Cheeger's (1999) metric differentiation theory. The class includes
the infinite diamond and both Laakso (2000) spaces. We also show that for each
of these structures there is a non-RNP Banach space which does not admit its
bilipschitz embedding.
  We prove that a dual Banach space does not have the RNP if and only if it
admits a bilipschitz embedding of the infinite diamond.
  The paper also contains related characterizations of reflexivity and the
infinite tree property.

28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
18
The categories of this paper are: econ
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio