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Algebra generated by derivatives. (English) Zbl 0534.26004

The following remarkable and deep result is proven: Whenever u:\(R\to R\) is a Baire 1 function there exist functions f, g, and h having a finite derivative everywhere such that \(u=f'+g'h'.\) Moreover, g’ may be taken to be bounded and f’ to be a Lebesgue function. Also if u is bounded f’, g’ and h’ can be taken to be bounded.
Reviewer: J.G.Ceder

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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