Symmetric continuity of real functions
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- by C. L. Belna PDF
- Proc. Amer. Math. Soc. 87 (1983), 99-102 Request permission
Abstract:
It is shown that the set of points where a real function is both symmetrically continuous and not continuous has inner measure zero but may have full outer measure.References
- Paul Erdős, Some remarks on subgroups of real numbers, Colloq. Math. 42 (1979), 119–120. MR 567551, DOI 10.4064/cm-42-1-119-120 H. Fried, Über die symmetrische Stetigkeit von Funktionen, Fund. Math. 29 (1937), 134-137. F. Hausdorff, Probléme #62, Fund. Math. 25 (1935), 578.
- David Preiss, A note on symmetrically continuous functions, Časopis Pěst. Mat. 96 (1971), 262–264, 300 (English, with Czech summary). MR 0306411
- E. M. Stein and A. Zygmund, On the differentiability of functions, Studia Math. 23 (1963/64), 247–283. MR 158955, DOI 10.4064/sm-23-3-247-283
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 87 (1983), 99-102
- MSC: Primary 26A15
- DOI: https://doi.org/10.1090/S0002-9939-1983-0677241-1
- MathSciNet review: 677241