Geodesic
Metric spaces nonembeddable into Banach spaces with the Radon–Nikodým property and thick families of geodesics
Mikhail I. Ostrovskii1
1 Department of Mathematics and Computer Science St. John's University 8000 Utopia Parkway Queens, NY 11439, U.S.A.
Fundamenta Mathematicae, Tome 227 (2014) no. 1, pp. 85-95.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We show that a geodesic metric space which does not admit bilipschitz embeddings into Banach spaces with the Radon–Nikodým property does not necessarily contain a bilipschitz image of a thick family of geodesics. This is done by showing that no thick family of geodesics is Markov convex, and comparing this result with results of Cheeger–Kleiner, Lee-Naor, and Li. The result contrasts with the earlier result of the author that any Banach space without the Radon–Nikodým property contains a bilipschitz image of a thick family of geodesics.
DOI : 10.4064/fm227-1-6
Keywords: geodesic metric space which does admit bilipschitz embeddings banach spaces radon nikod property does necessarily contain bilipschitz image thick family geodesics done showing thick family geodesics markov convex comparing result results cheeger kleiner lee naor result contrasts earlier result author banach space without radon nikod property contains bilipschitz image thick family geodesics

Mikhail I. Ostrovskii 1

1 Department of Mathematics and Computer Science St. John's University 8000 Utopia Parkway Queens, NY 11439, U.S.A. 
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Mikhail I. Ostrovskii. Metric spaces nonembeddable into Banach spaces with
 the Radon–Nikodým property and thick families of geodesics. Fundamenta Mathematicae, Tome 227 (2014) no. 1, pp. 85-95. doi : 10.4064/fm227-1-6. http://geodesic.mathdoc.fr/articles/10.4064/fm227-1-6/

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