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Optimal partitioning of a measurable space into countably many sets
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  • Published: December 1990

Optimal partitioning of a measurable space into countably many sets

  • Jerzy Legut1 &
  • Maciej Wilczynski1 

Probability Theory and Related Fields volume 86, pages 551–558 (1990)Cite this article

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  • 1 Citations

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Summary

A notion of an optimal partition of a measurable space into countably many sets according to given nonatomic probability measures is defined. It is shown that the set of optimal partitions is nonempty. Bounds for the optimal value are given and the set of optimal partitions is characterized. Finally, an example related to statistical decision theory is presented.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Technical University of Wroclaw, Wybrzeze Wyspianskiego 27, 50-370, Wroclaw, Poland

    Jerzy Legut & Maciej Wilczynski

Authors
  1. Jerzy Legut
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  2. Maciej Wilczynski
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Cite this article

Legut, J., Wilczynski, M. Optimal partitioning of a measurable space into countably many sets. Probab. Th. Rel. Fields 86, 551–558 (1990). https://doi.org/10.1007/BF01198174

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  • Received: 22 September 1988

  • Revised: 27 March 1990

  • Issue Date: December 1990

  • DOI: https://doi.org/10.1007/BF01198174

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Keywords

  • Stochastic Process
  • Probability Measure
  • Probability Theory
  • Mathematical Biology
  • Measurable Space
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