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

• Autorzy: N. H. Bingham , A. J. Ostaszewski
• Języki publikacji: EN

Abstrakty

EN

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 functions of Ash, Erdős and Rubel.

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 03E15: Descriptive set theory
• 26A03: Foundations: limits and generalizations, elementary topology of the line
• 28A05: Classes of sets (Borel fields, σ -rings, etc.), measurable sets, Suslin sets, analytic sets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 121
• Numer: 2
• Strony: 225-238

Daty

wydano

2010

Twórcy

autor

N. H. Bingham

• Mathematics Department, Imperial College London, London SW7 2AZ, UK

autor

A. J. Ostaszewski

• Mathematics Department, London School of Economics, Houghton Street, London WC2A 2AE, UK

Identyfikatory

DOI

10.4064/cm121-2-5