This is an announcement for the paper "Characterizations of the Radon-Nikodym Property in terms of inverse limits" by Jeff Cheeger and Bruce Kleiner.

Abstract: We show that a separable Banach space has the Radon-Nikodym Property if and only if it is isomorphic to the limit of an inverse system, V_1<--- V_2<---...<--- V_k<---..., where the V_i's are finite dimensional Banach spaces, and the bonding maps V_{k-1}<--- V_k are quotient maps. We also show that the inverse system can be chosen to be a good finite dimensional approximation (GFDA), a notion introduced our earlier paper "On the differentiability of Lipschtz maps from metric measure spaces into Banach spaces". As a corollary, it follows that the differentiation and bi-Lipschitz non-embedding theorems in that paper, which were proved for maps into GFDA targets, are optimal in the sense that they hold for targets with the Radon-Nikodym Property.

Archive classification: math.FA math.MG

Mathematics Subject Classification: 46B22;46G05

The source file(s), gfda.bbl: 1902 bytes

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/0706.3389

or

http://arXiv.org/abs/0706.3389

or by email in unzipped form by transmitting an empty message with subject line

uget 0706.3389

or in gzipped form by using subject line

get 0706.3389

to: math@arXiv.org.