The Cesàro-Denjoy-Pettis scale of integration (Q1064423)

This paper is related to an earlier one by the same authors [Acta Math. Hung. 42, 243-255 (1983; Zbl 0544.26003)]. Here they define the concepts of weak Peano derivatives, weak \(AC_ nG^*\) functions and an associated scale of Cesàro-Denjoy-Pettis integrals that generalizes a Denjoy-Pettis integral defined in a paper by the first author that is to appear. The scale is shown to be consistent and to generalize strictly the Lebesgue-Pettis integral, and the Cesàro-Denjoy-Bochner scale of their earlier paper. An integration by parts theorem is proved.