The McShane, PU and Henstock integrals of Banach valued functions

Authors: Di Piazza L.¹; Marraffa V.²

Source: Czechoslovak Mathematical Journal, Volume 52, Number 3, September 2002 , pp. 609-633(25)

Publisher: Springer

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Abstract:

Some relationships between the vector valued Henstock and McShane integrals are investigated. An integral for vector valued functions, defined by means of partitions of the unity (the PU-integral) is studied. In particular it is shown that a vector valued function is McShane integrable if and only if it is both Pettis and PU-integrable. Convergence theorems for the Henstock variational and the PU integrals are stated. The families of multipliers for the Henstock and the Henstock variational integrals of vector valued functions are characterized.

Keywords: Pettis; McShane; PU and Henstock integrals; variational integrals; multipliers

Language: English

Document Type: Research article

Affiliations: 1: Department of mathematics, University of Palermo, Via Archirafi 34, 90123 Palermo, Italy, dipiazza@math.unipa.it 2: Department of mathematics, University of Palermo, Via Archirafi 34, 90123 Palermo, Italy, marraffa@math.unipa.it

Publication date: 2002-09-01