## 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.

### MSC:

 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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### References:

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