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The Law of Large Numbers in a Metric Space with a Convex Combination Operation

Author

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  • Pedro Terán

    (Universidad de Zaragoza)

  • Ilya Molchanov

    (University of Bern)

Abstract

We consider a separable complete metric space equipped with a convex combination operation. For such spaces, we identify the corresponding convexification operator and show that the invariant elements for this operator appear naturally as limits in the strong law of large numbers. It is shown how to uplift the suggested construction to work with subsets of the basic space in order to develop a systematic way of proving laws of large numbers for such operations with random sets.

Suggested Citation

  • Pedro Terán & Ilya Molchanov, 2006. "The Law of Large Numbers in a Metric Space with a Convex Combination Operation," Journal of Theoretical Probability, Springer, vol. 19(4), pages 875-898, December.
    • Handle: RePEc:spr:jotpro:v:19:y:2006:i:4:d:10.1007_s10959-006-0043-0
    DOI: 10.1007/s10959-006-0043-0
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    References listed on IDEAS

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    1. Lisa Bloomer & Theodore P. Hill, 2002. "Random Probability Measures with Given Mean and Variance," Journal of Theoretical Probability, Springer, vol. 15(4), pages 919-937, October.
    2. Frank N. Proske & Madan L. Puri, 2002. "Strong Law of Large Numbers for Banach Space Valued Fuzzy Random Variables," Journal of Theoretical Probability, Springer, vol. 15(2), pages 543-551, April.
    3. Michael Monticino, 2001. "How to Construct a Random Probability Measure," International Statistical Review, International Statistical Institute, vol. 69(1), pages 153-167, April.
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    Cited by:

    1. Pedro Terán, 2016. "A Multivalued Strong Law of Large Numbers," Journal of Theoretical Probability, Springer, vol. 29(2), pages 349-358, June.

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