Displaying similar documents to “On a theorem of F. Riesz concerning the form of linear functionals”

Measure-Theoretic Characterizations of Certain Topological Properties

David Buhagiar, Emmanuel Chetcuti, Anatolij Dvurečenskij (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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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.

Borel extensions of Baire measures in ZFC

Menachem Kojman, Henryk Michalewski (2011)

Fundamenta Mathematicae

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We prove: 1) Every Baire measure on the Kojman-Shelah Dowker space admits a Borel extension. 2) If the continuum is not real-valued-measurable then every Baire measure on M. E. Rudin's Dowker space admits a Borel extension. Consequently, Balogh's space remains the only candidate to be a ZFC counterexample to the measure extension problem of the three presently known ZFC Dowker spaces.