On Borel, Baire and Lebesgue sets.
A. Abian (1979)
Publications de l'Institut Mathématique [Elektronische Ressource]
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Displaying similar documents to “The Borel structure of some non-Lebesgue sets”
On Borel, Baire and Lebesgue sets.
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.
Baire's Space of Permutations of n and Rearrangements of Series
Tibor Šalát (1999)
Matematički Vesnik
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On the difference property of Borel measurable functions
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.
On the prolongation of restrictions of Baire 1 functions to functions which are quasicontinuous and approximately continuous
Zbigniew Grande (2009)
Colloquium Mathematicae
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Let I ⊂ ℝ be an open interval and let A ⊂ I be any set. Every Baire 1 function f: I → ℝ coincides on A with a function g: I → ℝ which is simultaneously approximately continuous and quasicontinuous if and only if the set A is nowhere dense and of Lebesgue measure zero.
A Monogenic Baire Measure Need Not Be Completion Regular
Zdena Riečanová (1974)
Matematický časopis
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Non-separable Borel sets
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..........................................................................
A Baire function not countably decomposable into continuous functions
Roy O. Davies (1973)
Časopis pro pěstování matematiky
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