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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.
Mikhail I. Ostrovskii. "Metric spaces nonembeddable into Banach spaces with the Radon-Nikodým property and thick families of geodesics." Fundamenta Mathematicae 227.1 (2014): 85-95. <http://eudml.org/doc/282819>.
@article{MikhailI2014, abstract = {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.}, author = {Mikhail I. Ostrovskii}, journal = {Fundamenta Mathematicae}, keywords = {Banach space; bilipschitz embedding; Heisenberg group; Markov convexity; thick family of geodesics; Radon-Nikodým property}, language = {eng}, number = {1}, pages = {85-95}, title = {Metric spaces nonembeddable into Banach spaces with the Radon-Nikodým property and thick families of geodesics}, url = {http://eudml.org/doc/282819}, volume = {227}, year = {2014}, }
TY - JOUR AU - Mikhail I. Ostrovskii TI - Metric spaces nonembeddable into Banach spaces with the Radon-Nikodým property and thick families of geodesics JO - Fundamenta Mathematicae PY - 2014 VL - 227 IS - 1 SP - 85 EP - 95 AB - 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. LA - eng KW - Banach space; bilipschitz embedding; Heisenberg group; Markov convexity; thick family of geodesics; Radon-Nikodým property UR - http://eudml.org/doc/282819 ER -