Two theorems on measurable sets and sets having the Baire property
Malgorzata Filipczak (1992)
Czechoslovak Mathematical Journal
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Malgorzata Filipczak (1992)
Czechoslovak Mathematical Journal
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Harry I. Miller (1984)
Colloquium Mathematicae
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S. Basu (2000)
Czechoslovak Mathematical Journal
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Steinhaus [9] prove that if a set has a positive Lebesgue measure in the line then its distance set contains an interval. He obtained even stronger forms of this result in [9], which are concerned with mutual distances between points in an infinite sequence of sets. Similar theorems in the case we replace distance by mutual ratio were established by Bose-Majumdar [1]. In the present paper, we endeavour to obtain some results related to sets with Baire property in locally compact topological...
Harry I. Miller (1981)
Časopis pro pěstování matematiky
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Jan Jastrzębski (1983)
Fundamenta Mathematicae
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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...