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Sequences of capacities, with connections to large-deviation theory

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Abstract

Acapacity is a set function with some regularity properties on a Hausdorff spaceE. Many measures and all sup measures are examples. The set of capacities onE can be endowed with two natural topologies. The narrow topology corresponds to the weak topology for probability measures, while the vague topology corresponds to the vague topology for Radon measures. The connection between these topologies and large-deviation principles was noted in recent joint work with W. Vervaat. Here, the theory of capacities and their topologies is developed in directions which have implications for large-deviation theory.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, York University, M3J 1P3, North York, Ontario, Canada

    George L. O'Brien

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  1. George L. O'Brien
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This research was supported in part by the Natural Sciences and Engineering Research Council of Canada. Much of it was done while the author enjoyed the kind hospitality of the Delft University of Technology.

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O'Brien, G.L. Sequences of capacities, with connections to large-deviation theory. J Theor Probab 9, 19–35 (1996). https://doi.org/10.1007/BF02213733

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  • DOI: https://doi.org/10.1007/BF02213733

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