Metric spaces nonembeddable into Banach spaces with the Radon-Nikodým property and thick families 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 -