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

N. H. Bingham, and A. J. Ostaszewski. "Beyond Lebesgue and Baire II: Bitopology and measure-category duality." Colloquium Mathematicae 121.2 (2010): 225-238. <http://eudml.org/doc/283743>.

@article{N2010,
abstract = {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.},
author = {N. H. Bingham, A. J. Ostaszewski},
journal = {Colloquium Mathematicae},
keywords = {measure; category; measure-category duality; Baire space; Baire property; Baire category theorem; density topology},
language = {eng},
number = {2},
pages = {225-238},
title = {Beyond Lebesgue and Baire II: Bitopology and measure-category duality},
url = {http://eudml.org/doc/283743},
volume = {121},
year = {2010},
}

TY - JOUR
AU - N. H. Bingham
AU - A. J. Ostaszewski
TI - Beyond Lebesgue and Baire II: Bitopology and measure-category duality
JO - Colloquium Mathematicae
PY - 2010
VL - 121
IS - 2
SP - 225
EP - 238
AB - 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.
LA - eng
KW - measure; category; measure-category duality; Baire space; Baire property; Baire category theorem; density topology
UR - http://eudml.org/doc/283743
ER -