Sequential closure in the space of measures
General Topology
2012-09-21 v2
Abstract
We show that there is a compact topological space carrying a measure which is not a weak* limit of finitely supported measures but is in the sequential closure of the set of such measures. We construct compact spaces with measures of arbitrarily high levels of complexity in this sequential hierarchy. It follows that there is a compact space in which the sequential closure cannot be obtained in countably many steps. However, we show that this is not the case for our spaces where the sequential closure is always obtained in countably many steps.
Cite
@article{arxiv.1203.4270,
title = {Sequential closure in the space of measures},
author = {Piotr Borodulin-Nadzieja and Omar Selim},
journal= {arXiv preprint arXiv:1203.4270},
year = {2012}
}
Comments
(18 pages, a gap in an argument from the previous version fixed)