A Volterra type derivative of the Lebesgue integral. (English) Zbl 0789.28005

Using functions of bounded variation, a Volterra type derivative of the linear functional \(F\) associated to a Lebesgue integrable function \(f\) over an open subset of \(\mathbb{R}^ n\) is defined. It is shown that this Volterra type derivative of \(F\) is equal to \(F\) almost everywhere when \(f\) is locally bounded. Such a result is useful in studying some properties of some conditionally convergent integrals.


28A15 Abstract differentiation theory, differentiation of set functions
46G05 Derivatives of functions in infinite-dimensional spaces
26A42 Integrals of Riemann, Stieltjes and Lebesgue type
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