Measure-theoretic characterizations of certain topological properties

Abstract

It is shown that Cech completeness, ultra completeness and local compactness can be defined by demanding that certain equivalences hold between certain lasses of Baire measures or by demanding that certain lasses 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 real compact spaces.