Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

$ 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
DOI: https://doi.org/10.1090/S0002-9939-1984-0754715-7
MathSciNet review: 754715
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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)
  • [4] -, Smoothness and differentiability in $ {L_p}$, Studia Math. 25 (1964), 81-91. MR 0181715 (31:5942)
  • [5] R. J. O'Malley, Baire* 1, Darboux functions, Proc. Amer. Math. Soc. 60 (1976), 187-192. MR 0417352 (54:5405)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 26A15

Retrieve articles in all journals with MSC: 26A15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0754715-7
Keywords: Smooth, $ {L_p}$ smooth, approximately continuous
Article copyright: © Copyright 1984 American Mathematical Society

American Mathematical Society