It is shown that there is no closed convex bounded non-dentable subset K of such that on subsets of K the PCP and the RNP are equivalent properties. Then applying the Schachermayer-Rosenthal theorem, we conclude that every non-dentable K contains a non-dentable subset L so that on L the weak topology coincides with the norm topology. It follows from known results that the RNP and the KMP are equivalent on subsets of .
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm203-3-1,
author = {Pericles D. Pavlakos and Minos Petrakis},
title = {On the structure of non-dentable subsets of $C($\omega$^{$\omega$^{k}})$
},
journal = {Studia Mathematica},
volume = {204},
year = {2011},
pages = {205-222},
zbl = {1229.46016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm203-3-1}
}
Pericles D. Pavlakos; Minos Petrakis. On the structure of non-dentable subsets of $C(ω^{ω^{k}})$
. Studia Mathematica, Tome 204 (2011) pp. 205-222. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm203-3-1/