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Proceedings of the American Mathematical Society

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A measure theoretic variant of Blumberg's theorem


Author: Jack B. Brown
Journal: Proc. Amer. Math. Soc. 66 (1977), 266-268
MSC: Primary 26A24
DOI: https://doi.org/10.1090/S0002-9939-1977-0463377-4
MathSciNet review: 0463377
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Abstract: It is the purpose of this note to present a measure theoretic variant of Blumberg's theorem about continuous restrictions of arbitrary real functions.


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

  • [1] H. Blumberg, New properties of all real functions, Trans. Amer. Math. Soc. 24 (1922), 113-128. MR 1501216
  • [2] -, Arbitrary point transformations, Duke Math. J. 11 (1944), 671-685. MR 0011714 (6:205b)
  • [3] J. B. Brown, Metric spaces in which a strengthened form of Blumberg's theorem holds, Fund. Math. 71 (1971), 243-253. MR 0292024 (45:1112)
  • [4] -, Lusin density and Ceder's differentiable restrictions of arbitrary real functions, Fund. Math. 84 (1974), 35-45. MR 0335699 (49:479)
  • [5] J. G. Ceder, Differentiable roads for real functions, Fund. Math. 65 (1969), 351-358. MR 0251167 (40:4398)
  • [6] W. Sierpiński and A. Zygmund, Sur une function qui est discontinue sur tout ensemble de puissance du continu, Fund. Math. 4 (1923), 316-318.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0463377-4
Article copyright: © Copyright 1977 American Mathematical Society

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