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Non-weak compactness of the integration map for vector measures

1993
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Journal of the Australian Mathematical Society
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Let m be a vector measure with values in a Banach space X . If L l (m) denotes the space of all m integrable functions then, with respect to the mean convergence topology, L l (m) is a Banach space. A natural operator associated with m is its integration map I m which sends each / of L l (m) to the element ffdm (of X). Many properties of the (continuous) operator I m are closely related to the nature of the space L (m). In general, it is difficult to identify L (m). We aim to exhibit

doi:10.1017/s1446788700031797
fatcat:2jbtf4mwqfdrdkejbgezjrdwtm