A remark on Slutsky's theorem
Freddy Delbaen (1998)
Séminaire de probabilités de Strasbourg
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Freddy Delbaen (1998)
Séminaire de probabilités de Strasbourg
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Steven Shreve (1981)
Fundamenta Mathematicae
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Ryszard Engelking, Włodzimierz Holsztyński, Roman Sikorski (1966)
Colloquium Mathematicum
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John B. Walsh (1971)
Séminaire de probabilités de Strasbourg
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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.
Miloslav Duchoň (1974)
Matematický časopis
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Michael Rice, George Reynolds (1980)
Fundamenta Mathematicae
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Vassilios Gregoriades (2012)
Fundamenta Mathematicae
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We present the effective version of the theorem about turning Borel sets in Polish spaces into clopen sets while preserving the Borel structure of the underlying space. We show that under some conditions the emerging parameters can be chosen in a hyperarithmetical way and using this we obtain some uniformity results.
Adam Jakubowski (1986)
Annales de l'I.H.P. Probabilités et statistiques
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