summary: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).
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机译：摘要：我们研究与Banach空间值测度有关的Banach空间值函数的集成。我们将注意力集中在对Birkhoff和McShane积分的这种设置的自然扩展上。多布拉科夫首先以$ S ^ {*} $-integral的名义考虑了Birkhoff积分的相应推广。我们的主要结果表明，在可以定义后面的概念的情况下，$ S ^ {*} $-可积性意味着McShane可积性。我们还表明，当且仅当函数是Dobrakov可积（即Bartle *可积）时，函数才可测量且McShane可积。
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