On Borel Mappings and Baire Functions
نویسندگان
چکیده
منابع مشابه
When are Borel functions Baire functions ?
The following two theorems give the flavour of what will be proved. THEOREM. Let Y be a complete metric space. Then the families of first Baire class functions and of first Borel class functions from [0, 1] to Y coincide if and only if Y is connected and locally connected. THEOREM. Let Y be a separable metric space. Then the families of second Baire class functions and of second Borel class fun...
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All spaces considered are metric separable and are denoted usually by the letters X, Y , or Z. ω stands for the set of all natural numbers. If a metric separable space is additionally complete, we call it Polish; if it is a continuous image of ω or, equivalently, of a Polish space, it is called Souslin. The main subject of the present paper is the structure of Baire class 1 functions. Recent de...
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We prove: (1) Every Baire measure on the Kojman-Shelah Dowker space [10] admits a Borel extension. (2) If the continuum is not a real-valued measurable cardinal then every Baire measure on the M. E. Rudin Dowker space [16] admits a Borel extension. Consequently, Balogh’s space [3] remains as the only candidate to be a ZFC counterexample to the measure extension problem of the three presently kn...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1974
ISSN: 0002-9947
DOI: 10.2307/1996801