It is shown that Čech completeness, ultracompleteness and local compactness can be defined by demanding that certain equivalences hold between certain classes of Baire measures or by demanding that certain classes of Baire measures have non-empty support. This shows that these three topological properties are measurable, similarly to the classical examples of compact spaces, pseudo-compact spaces and realcompact spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-1-9,
author = {David Buhagiar and Emmanuel Chetcuti and Anatolij Dvure\v censkij},
title = {Measure-Theoretic Characterizations of Certain Topological Properties},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {53},
year = {2005},
pages = {99-109},
zbl = {1113.28012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-1-9}
}
David Buhagiar; Emmanuel Chetcuti; Anatolij Dvurečenskij. Measure-Theoretic Characterizations of Certain Topological Properties. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) pp. 99-109. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-1-9/