Geodesic
On integration of vector functions with respect to vector measures
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 3, pp. 805-825 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We study integration of Banach space-valued functions with respect to Banach space-valued measures. We focus our attention on natural extensions to this setting of the Birkhoff and McShane integrals. The corresponding generalization of the Birkhoff integral was first considered by Dobrakov under the name $S^{*}$-integral. Our main result states that $S^{*}$-integrability implies McShane integrability in contexts in which the later notion is definable. We also show that a function is measurable and McShane integrable if and only if it is Dobrakov integrable (i.e. Bartle *-integrable).
We study integration of Banach space-valued functions with respect to Banach space-valued measures. We focus our attention on natural extensions to this setting of the Birkhoff and McShane integrals. The corresponding generalization of the Birkhoff integral was first considered by Dobrakov under the name $S^{*}$-integral. Our main result states that $S^{*}$-integrability implies McShane integrability in contexts in which the later notion is definable. We also show that a function is measurable and McShane integrable if and only if it is Dobrakov integrable (i.e. Bartle *-integrable).
Classification : 28B05, 46G10
Keywords: Bartle $^*$-integral; Dobrakov integral; McShane integral; Birkhoff integral; $S^*$-integral 
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Rodríguez, José. On integration of vector functions with respect to vector measures. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 3, pp. 805-825. http://geodesic.mathdoc.fr/item/CMJ_2006_56_3_a1/

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