Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4616435 | Journal of Mathematical Analysis and Applications | 2014 | 5 Pages |
Abstract
Banach spaces without the Radon-Nikodým property are characterized as spaces containing bilipschitz images of thick families of geodesics defined as follows. A family T of geodesics joining points u and v in a metric space is called thick if there is α>0 such that for every gâT and for any finite collection of points r1,â¦,rn in the image of g, there is another uv-geodesic gËâT satisfying the conditions: gË also passes through r1,â¦,rn, and, possibly, has some more common points with g. On the other hand, there is a finite collection of common points of g and gË which contains r1,â¦,rn and is such that the sum of maximal deviations of the geodesics between these common points is at least α.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Mikhail Ostrovskii,