Typical continuous functions are virtually nonmonotone
Abstract: For every porosity premeasure , a typical continuous function meets every monotone function in a bilaterally strongly -porous set. The statement does not remain valid if we replace the class of monotone functions by the class of absolutely continuous functions.
- [H] J. Haussermann, Generalized porosity characteristics of a residual set of continuous functions, Ph. D. dissertation, University of California, Santa Barbara, 1984.
- [T] 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, 10.1090/conm/042/807990
Keywords: Typical continuous functions, intersections with monotone functions, porous sets
Article copyright: © Copyright 1985 American Mathematical Society