On a theorem of S. Banach.
Neeb, Karl-Hermann (1997)
Journal of Lie Theory
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Displaying similar documents to “On the difference property of Borel measurable functions”
On a theorem of S. Banach.
Classification of -ideals
Marek Balcerzak (1987)
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A measurable selection theorem
John Burgess (1980)
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On Baire approximations of normal integrands
Anna Kucia, Andrzej Nowak (1989)
Commentationes Mathematicae Universitatis Carolinae
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On Weakly Measurable Functions
Szymon Żeberski (2005)
Bulletin of the Polish Academy of Sciences. Mathematics
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We show that if T is an uncountable Polish space, 𝓧 is a metrizable space and f:T→ 𝓧 is a weakly Baire measurable function, then we can find a meagre set M ⊆ T such that f[T∖M] is a separable space. We also give an example showing that "metrizable" cannot be replaced by "normal".
The Borel structure of some non-Lebesgue sets
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.
Decomposition in the product of a measure space and a Polish space
J. Bourgain (1979)
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Solution of Kuratowski's problem on function having the Baire property, I
Ryszard Frankiewicz, Kenneth Kunen (1987)
Fundamenta Mathematicae
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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.
Gradients of Borel functions
B. Bongiorno, P. Vetro (1978)
Colloquium Mathematicae
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Functions Equivalent to Borel Measurable Ones
Andrzej Komisarski, Henryk Michalewski, Paweł Milewski (2010)
Bulletin of the Polish Academy of Sciences. Mathematics
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Let X and Y be two Polish spaces. Functions f,g: X → Y are called equivalent if there exists a bijection φ from X onto itself such that g∘φ = f. Using a theorem of J. Saint Raymond we characterize functions equivalent to Borel measurable ones. This characterization answers a question asked by M. Morayne and C. Ryll-Nardzewski.