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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

$ C\sp{\infty }$-functions need not be bimeasurable


Author: R. B. Darst
Journal: Proc. Amer. Math. Soc. 27 (1971), 128-132
MSC: Primary 26.80
DOI: https://doi.org/10.1090/S0002-9939-1971-0267060-4
MathSciNet review: 0267060
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Abstract: A real valued $ {C^\infty }$-function $ f$ is constructed on the interval $ I = [0,1]$ such that some Borel subsets of $ I$ are mapped by $ f$ onto non-Borel sets.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0267060-4
Keywords: Bimeasurable function, Borel function, Borel set, $ {C^\infty }$-function, real numbers
Article copyright: © Copyright 1971 American Mathematical Society