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

Pedro Terán () and Ilya Molchanov ()
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Pedro Terán: Universidad de Zaragoza
Ilya Molchanov: University of Bern

Journal of Theoretical Probability, 2006, vol. 19, issue 4, 875-898

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.

Keywords: Convexification; decomposability; Doss expectation; law of large numbers; random sets (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/s10959-006-0043-0

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