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On integration in Banach spaces. XII: Integration with respect to polymeasures. (English) Zbl 0793.28007

The paper is a continuation of an imposing series of papers [see, e.g., Part XI (1990) reviewed above] devoted to a type of integral in Banach spaces named Dobrakov integral. The present part contains first a measurability theory, then a weak and \(\text{weak}^*\) integration theory, and finally the monotone convergence theorem and a characterization of the space of integrable functions. The explanation is quite complicated depending on some previously exposed facts. On the other hand many previous results of the author are remarkably improved. (See also the following review).

MSC:

28B05 Vector-valued set functions, measures and integrals
46G10 Vector-valued measures and integration
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References:

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