A measure theoretic variant of Blumberg’s theorem

Brown, Jack B.

doi:10.1090/S0002-9939-1977-0463377-4

A measure theoretic variant of Blumberg’s theorem
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by Jack B. Brown

Proc. Amer. Math. Soc. 66 (1977), 266-268

DOI: https://doi.org/10.1090/S0002-9939-1977-0463377-4

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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

Henry Blumberg, New properties of all real functions, Trans. Amer. Math. Soc. 24 (1922), no. 2, 113–128. MR 1501216, DOI 10.1090/S0002-9947-1922-1501216-9
Henry Blumberg, Arbitrary point transformations, Duke Math. J. 11 (1944), 671–685. MR 11714
Jack B. Brown, Metric spaces in which a strengthened form of Blumberg’s theorem holds, Fund. Math. 71 (1971), no. 3, 243–253. MR 292024, DOI 10.4064/fm-71-3-243-253
Jack B. Brown, Lusin density and Ceder’s differentiable restrictions of arbitrary real functions, Fund. Math. 84 (1974), no. 1, 35–45. MR 335699, DOI 10.4064/fm-84-1-35-45
Jack G. Ceder, Differentiable roads for real functions, Fund. Math. 65 (1969), 351–358. MR 251167, DOI 10.4064/fm-65-3-351-358

Sur une function qui est discontinue sur tout ensemble de puissance du continu

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