Typical continuous functions are virtually nonmonotone
HTML articles powered by AMS MathViewer
- by P. Humke and M. Laczkovich
- Proc. Amer. Math. Soc. 94 (1985), 244-248
- DOI: https://doi.org/10.1090/S0002-9939-1985-0784172-7
- PDF | 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
Bibliographic 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