Displaying similar documents to “Duality of measure and category in infinite-dimensional separable Hilbert space ℓ 2 .”

Some results on projection of planar sets

Dilip Kumar Ganguly, M. Majumdar (1998)

Czechoslovak Mathematical Journal

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In this paper we define certain types of projections of planar sets and study some properties of such projections.

Beyond Lebesgue and Baire II: Bitopology and measure-category duality

N. H. Bingham, A. J. Ostaszewski (2010)

Colloquium Mathematicae

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We re-examine measure-category duality by a bitopological approach, using both the Euclidean and the density topologies of the line. We give a topological result (on convergence of homeomorphisms to the identity) obtaining as a corollary results on infinitary combinatorics due to Kestelman and to Borwein and Ditor. We hence give a unified proof of the measure and category cases of the Uniform Convergence Theorem for slowly varying functions. We also extend results on very slowly varying...

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.