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Proceedings of the American Mathematical Society

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$ L\sb{p}$ smoothness and approximate continuity

Authors: Michael J. Evans and Paul D. Humke
Journal: Proc. Amer. Math. Soc. 92 (1984), 258-262
MSC: Primary 26A15
MathSciNet review: 754715
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Abstract: It is known that a measurable smooth function can have only countably many points of discontinuity. A measurable function is constructed here having the property of being $ {L_p}$ smooth and having uncountably many points of $ {L_p}$ (in fact, approximate) discontinuity.

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

  • [1] M. J. Evans and P. D. Humke, A pathological approximately smooth function (submitted).
  • [2] M. J. Evans and L. Larson, The continuity of symmetric and smooth functions, Acta Math. Acad. Sci. Hungar. (to appear). MR 733857 (85h:26005)
  • [3] C. J. Neugebauer, Symmetric, continuous and smooth functions, Duke Math. J. 31 (1964), 23-32. MR 0158035 (28:1263)
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Keywords: Smooth, $ {L_p}$ smooth, approximately continuous
Article copyright: © Copyright 1984 American Mathematical Society

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