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Keywords:
scalar derivative; approximate scalar derivative; absolute continuity; bounded variation; $VBG$ function; $ACG$ function; Pettis integral; Denjoy-Pettis integral
scalar derivative; approximate scalar derivative; absolute continuity; bounded variation; $VBG$ function; $ACG$ function; Pettis integral; Denjoy-Pettis integral
Summary:
In this paper two Denjoy type extensions of the Pettis integral are defined and studied. These integrals are shown to extend the Pettis integral in a natural way analogous to that in which the Denjoy integrals extend the Lebesgue integral for real-valued functions. The connection between some Denjoy type extensions of the Pettis integral is examined.
References:
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