Geodesic
The McShane, PU and Henstock integrals of Banach valued functions
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 3, pp. 609-633 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 integrals of vector valued functions are characterized.
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.
Classification : 26A39, 26B30, 28B05, 46G10
Keywords: Pettis; McShane; PU and Henstock integrals; variational integrals; multipliers 
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     author = {Di Piazza, Luisa and Marraffa, V.},
     title = {The {McShane,} {PU} and {Henstock} integrals of {Banach} valued functions},
     journal = {Czechoslovak Mathematical Journal},
     pages = {609--633},
     year = {2002},
     volume = {52},
     number = {3},
     mrnumber = {1923266},
     zbl = {1011.28007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2002_52_3_a14/}
}
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Di Piazza, Luisa; Marraffa, V. The McShane, PU and Henstock integrals of Banach valued functions. Czechoslovak Mathematical Journal, Tome 52 (2002) no. 3, pp. 609-633. http://geodesic.mathdoc.fr/item/CMJ_2002_52_3_a14/