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Families of vector measures of uniformly bounded variation

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Abstract.

We characterize families of vector measures of uniformly bounded variation and semivariation in terms of additivity properties. A classical theorem of Rickart and a simplified proof of Nikodým’s boundedness theorem follow.

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Authors and Affiliations

  1. Department of Mathematics, Agder University College, Servicebox 422, 4604, Kristiansand, Norway

    Olav Nygaard

  2. Institute of Pure Mathematics, University of Tartu, J. Liivi 2, 50409, Tartu, Estonia

    Märt Põldvere

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  1. Olav Nygaard
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  2. Märt Põldvere
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Correspondence to Olav Nygaard.

Additional information

Received: 3 January 2006; Revised: 31 March 2006

The second named author was supported by Estonian Science Foundation Grant 5704.

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Nygaard, O., Põldvere, M. Families of vector measures of uniformly bounded variation. Arch. Math. 88, 57–61 (2007). https://doi.org/10.1007/s00013-006-1859-7

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  • DOI: https://doi.org/10.1007/s00013-006-1859-7

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