On measures in fibre spaces
Anthony Karel Seda (1980)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Anthony Karel Seda (1980)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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A. Goetz (1959)
Colloquium Mathematicae
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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.
R. Dudley (1966)
Studia Mathematica
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Jan Mařík (1957)
Czechoslovak Mathematical Journal
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Vladimír Olejček (1974)
Matematický časopis
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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.