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Convergence in measure under finite additivity

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Abstract

We investigate the possibility of replacing the topology of convergence in probability with convergence in L 1, upon a change of the underlying measure under finite additivity. We establish conditions for the continuity of linear operators and convergence of measurable sequences, including a finitely additive analog of Komlós Lemma. We also prove several topological implications. Eventually, a characterization of continuous linear functionals on the space of measurable functions is obtained.

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Authors and Affiliations

  1. Department of Economics, Statistics and Management, Università Milano Bicocca, Building U7, Room 2097, via Bicocca degli Arcimboldi 8, 20126, Milano, Italy

    Gianluca Cassese

  2. University of Lugano, via G. Buffi, 13, 6904, Lugano, Switzerland

    Gianluca Cassese

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  1. Gianluca Cassese
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Correspondence to Gianluca Cassese.

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Cassese, G. Convergence in measure under finite additivity. Sankhya A 75, 171–193 (2013). https://doi.org/10.1007/s13171-013-0030-3

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  • DOI: https://doi.org/10.1007/s13171-013-0030-3

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