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.
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Di Piazza, L., Marraffa, V. The McShane, PU and Henstock integrals of Banach valued functions. Czechoslovak Mathematical Journal 52, 609–633 (2002). https://doi.org/10.1023/A:1021736031567
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DOI: https://doi.org/10.1023/A:1021736031567