On Henstock's inner variation and strong derivatives.
Introducing the concept of McShane differentiability of a function \(F:[a,b]\to \mathbb R\) the author studies the Lebesgue integrability of the McShane derivative of \(F\). Sets of inner variation zero and the strong Lusin condition are involved. It is mentioned that the results can be presented in the same way also for functions \(F\) having values in a Banach space when speaking about the Bochner integral. At the end of the paper it is shown how the results can be used in classical stochastic analysis.
scientific article; zbMATH DE number 2084005