Note on generalized multiple Perron integral
Josef Král (1985)
Časopis pro pěstování matematiky
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Josef Král (1985)
Časopis pro pěstování matematiky
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R. Gordon (1989)
Studia Mathematica
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Luisa Di Piazza, Valeria Marraffa (2002)
Czechoslovak Mathematical Journal
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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...
M. Wilhelm (1975)
Colloquium Mathematicae
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Richard Reynolds, Charles W. Swartz (2004)
Mathematica Bohemica
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The classical Vitali convergence theorem gives necessary and sufficient conditions for norm convergence in the space of Lebesgue integrable functions. Although there are versions of the Vitali convergence theorem for the vector valued McShane and Pettis integrals given by Fremlin and Mendoza, these results do not involve norm convergence in the respective spaces. There is a version of the Vitali convergence theorem for scalar valued functions defined on compact intervals in given by...