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A generalized Henstock integral. (English) Zbl 1084.26004

A specific integration based on the concept of \(\delta\)-fine tagged \(k\)-partitions is defined for functions \(U:[a,b]^{k=1} \to \mathbb R^n\) in the flavor of Henstock-Kurzweil integration. The resulting integral is called the \(GH_k\) integral. If \(k=1\) then the \(GH_1\) integral coincides with the integral described in the reviewers book “Generalized ordinary differential equations” (1992; Zbl 0781.34003). Basic results for the \(GH_k\) integral are presented (Saks-Henstock lemma, Cauchy extension) and in the introduction other similar concepts of integration are discussed.

MSC:

26A39 Denjoy and Perron integrals, other special integrals
26A42 Integrals of Riemann, Stieltjes and Lebesgue type

Citations:

Zbl 0781.34003
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