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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Typical continuous functions are virtually nonmonotone
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by P. Humke and M. Laczkovich PDF
Proc. Amer. Math. Soc. 94 (1985), 244-248 Request permission

Abstract:

For every porosity premeasure $\phi$, a typical continuous function meets every monotone function in a bilaterally strongly $\phi$-porous set. The statement does not remain valid if we replace the class of monotone functions by the class of absolutely continuous functions.
References
    J. Haussermann, Generalized porosity characteristics of a residual set of continuous functions, Ph. D. dissertation, University of California, Santa Barbara, 1984.
  • B. S. Thomson, On the level set structure of a continuous function, Classical real analysis (Madison, Wis., 1982) Contemp. Math., vol. 42, Amer. Math. Soc., Providence, RI, 1985, pp. 187–190. MR 807990, DOI 10.1090/conm/042/807990
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 94 (1985), 244-248
  • MSC: Primary 26A15; Secondary 26A48
  • DOI: https://doi.org/10.1090/S0002-9939-1985-0784172-7
  • MathSciNet review: 784172