Characteristic functions and products of derivatives. (English) Zbl 0732.26007

Mařík, Jan

Real Anal. Exch. 16(1990/91), No. 1, 245-254 (1991).

The following Theorem is proven: For a subset S of the reals R the following are mutually equivalent: (1) the characteristic function of S is a product of finitely many derivatives; (2) S is ambiguous and \(T=R\setminus S\) is porous; (3) there exist derivatives f and g such that \(f=g=1\) on S and \(fg=0\) on T.

Reviewer: J.G.Ceder (Santa Barbara)

MSC:

26A24	Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
26A21	Classification of real functions; Baire classification of sets and functions

Keywords:

ambiguous set; porous set; characteristic function; product of finitely many derivatives