Baire's Space of Permutations of n and Rearrangements of Series
Tibor Šalát (1999)
Matematički Vesnik
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Tibor Šalát (1999)
Matematički Vesnik
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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.
A. H. Stone
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CONTENTS1. Introduction.................................................................................. 32. Baire spaces................................................................................ 53. The basic theorem..................................................................... 94. Cardinality properties; invariance of weight........................... 165. Classification of absolute Borel sets..................................... 226. Characterizations..........................................................................
Don L. Hancock (2004)
Colloquium Mathematicae
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For a given function in some classes related to real derivatives, we examine the structure of the set of points which are not Lebesgue points. In particular, we prove that for a summable approximately continuous function, the non-Lebesgue set is a nowhere dense nullset of at most Borel class 4.
Jayne, J. E.
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Lorenz Halbeisen (2001)
Colloquium Mathematicae
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We call a subset S of a topological vector space V linearly Borel if for every finite number n, the set of all linear combinations of S of length n is a Borel subset of V. It is shown that a Hamel basis of an infinite-dimensional Banach space can never be linearly Borel. This answers a question of Anatoliĭ Plichko.
Ireneusz Recław (1989)
Fundamenta Mathematicae
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Howard Becker (1987)
Fundamenta Mathematicae
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B. Rao (1970)
Fundamenta Mathematicae
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A. Abian (1979)
Publications de l'Institut Mathématique [Elektronische Ressource]
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Hiroshi Fujita, Tamás Mátrai (2010)
Fundamenta Mathematicae
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If an atomlessly measurable cardinal exists, then the class of Lebesgue measurable functions, the class of Borel functions, and the Baire classes of all orders have the difference property. This gives a consistent positive answer to Laczkovich's Problem 2 [Acta Math. Acad. Sci. Hungar. 35 (1980)]. We also give a complete positive answer to Laczkovich's Problem 3 concerning Borel functions with Baire-α differences.
Stuart Zoble (2006)
Fundamenta Mathematicae
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We show that ω₁-Universally Baire self-justifying systems are fully Universally Baire under the Weak Stationary Reflection Principle for Pairs. This involves analyzing the notion of a weakly captured set of reals, a weakening of the Universal Baire Property.
R. Willmott (1971)
Fundamenta Mathematicae
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