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Proceedings of the American Mathematical Society

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$ 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.


References [Enhancements On Off] (What's this?)

  • [1] R. B. Darst, A characterization of bimeasurable functions in terms of universally measurable sets, Proc. Amer. Math. Soc. (to appear). MR 0274694 (43:456)
  • [2] -, On the $ 1{\text{ - }}1$ sum of two Borel sets, Proc. Amer. Math. Soc. 25 (1970), 914. MR 0263638 (41:8239)
  • [3] N. Lusin, Leçons sur les ensembles analytiques et leurs applications, Gauthier-Villars, Paris, 1930.
  • [4] Roger Purves, Bimeasurable functions, Fund. Math. 58 (1966), 149-157. MR 33 #7487. MR 0199339 (33:7487)

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Additional Information

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

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