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How can we recover Baire class one functions?
Author(s) -
Lecomte Dominique
Publication year - 2003
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300014881
Subject(s) - baire space , baire measure , baire category theorem , mathematics , separable space , metrization theorem , characterization (materials science) , class (philosophy) , banach space , space (punctuation) , pure mathematics , simple (philosophy) , function (biology) , discrete mathematics , set (abstract data type) , complete metric space , mathematical analysis , computer science , philosophy , materials science , epistemology , artificial intelligence , evolutionary biology , biology , programming language , nanotechnology , operating system
Let X and Y be separable metrizable spaces, and f: X→Y a function. It is wished to recover f from its values on a small set via a simple algorithm. It is shown that this is possible if f is Baire class one, and in fact a characterization is obtained. This leads to the study of sets of Baire class one functions and to a characterization of the separability of the dual space of an arbitrary Banach space.