$C^{\infty }$-functions need not be bimeasurable
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- by R. B. Darst PDF
- Proc. Amer. Math. Soc. 27 (1971), 128-132 Request permission
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
- R. B. Darst, A characterization of bimeasurable functions in terms of universally measurable sets, Proc. Amer. Math. Soc. 27 (1971), 566β571. MR 274694, DOI 10.1090/S0002-9939-1971-0274694-X
- Richard B. Darst, On the $1-1$ sum of two Borel sets, Proc. Amer. Math. Soc. 25 (1970), 914. MR 263638, DOI 10.1090/S0002-9939-1970-0263638-1 N. Lusin, Leçons sur les ensembles analytiques et leurs applications, Gauthier-Villars, Paris, 1930.
- R. Purves, Bimeasurable functions, Fund. Math. 58 (1966), 149β157. MR 199339, DOI 10.4064/fm-58-2-149-157
Additional Information
- © Copyright 1971 American Mathematical Society
- 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