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

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
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