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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
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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.


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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