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Functions of the First Baire Class
Author(s) -
Rogers C. A.
Publication year - 1988
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-37.3.535
Subject(s) - baire measure , extension (predicate logic) , baire space , baire category theorem , class (philosophy) , mathematics , complete metric space , property (philosophy) , metric (unit) , metric space , space (punctuation) , pure mathematics , function (biology) , discrete mathematics , computer science , economics , philosophy , operations management , epistemology , evolutionary biology , biology , programming language , artificial intelligence , operating system
Let f be a function of the first Borel class mapping the metric space X to the metric space Y : Hansell has claimed that, if f is σ‐discrete and Y has the extension property for X , then f is necessarily of the first Baire class; but his proof is incomplete. It is shown that the result is true if Y also has a certain local extension property for X . Conditions are given that ensure that Y has both extension properties for X .