It has been an open question since 1997 whether, and under what assumptions on the underlying space, extreme topological measures are dense in the set of all topological measures on the space. The present paper answers this question. The main result implies that extreme topological measures are dense on a variety of spaces, including spheres, balls and projective planes.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm192-2-4,
author = {S. V. Butler},
title = {Extreme topological measures},
journal = {Fundamenta Mathematicae},
volume = {189},
year = {2006},
pages = {141-153},
zbl = {1116.28011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm192-2-4}
}
S. V. Butler. Extreme topological measures. Fundamenta Mathematicae, Tome 189 (2006) pp. 141-153. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm192-2-4/