Baire one, null functions. (English) Zbl 0587.26004

Bruckner, A. M.; Mařík, J.; Weil, C. E.

Classical real analysis, Proc. Spec. Sess., 794th Meet. AMS, Madison/Wis. 1982, Contemp. Math. 42, 29-41 (1985).

[For the entire collection see Zbl 0565.00007.]
Authors’ summary: It is proved that a Baire one function which is zero almost everywhere can be written as the product of two derivatives. Moreover, if the function is nonnegative, then the factors can be selected to be nonnegative. In both cases the factors can be chosen to have arbitrarily small \(L^ p\) norm for \(1\leq p<\infty\).

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

Keywords:

Baire one function; product of two derivatives

Citations:

Zbl 0565.00007