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On the right preponderant limit. (English) Zbl 1110.26005

The author investigates the right preponderent limit of a function and generalizes the result of D. N. Sarkhel on Baire one functions. The main result is the theorem: Let \(F:R\rightarrow R\) be a measurable function (in the Lebesgue sense). If a function \(f:R\rightarrow R\) is such that \(f(x)\in L_{r}(F,x)\) for all \(x\in R\), then \(f\) is of Baire one class.

MSC:

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