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Proceedings of the American Mathematical Society

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Symmetric continuity of real functions

Author: C. L. Belna
Journal: Proc. Amer. Math. Soc. 87 (1983), 99-102
MSC: Primary 26A15
MathSciNet review: 677241
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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 [Enhancements On Off] (What's this?)

  • [1] Paul Erdős, Some remarks on subgroups of real numbers, Colloq. Math. 42 (1979), 119–120. MR 567551
  • [2] H. Fried, Über die symmetrische Stetigkeit von Funktionen, Fund. Math. 29 (1937), 134-137.
  • [3] F. Hausdorff, Probléme #62, Fund. Math. 25 (1935), 578.
  • [4] David Preiss, A note on symmetrically continuous functions, Časopis Pěst. Mat. 96 (1971), 262–264, 300 (English, with Czech summary). MR 0306411
  • [5] E. M. Stein and A. Zygmund, On the differentiability of functions, Studia Math. 23 (1963/1964), 247–283. MR 0158955

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Article copyright: © Copyright 1983 American Mathematical Society