The Law of Large Numbers in a Metric Space with a Convex Combination Operation
Terán, Pedro ; Molchanov, Ilya
In: Journal of Theoretical Probability, 2006, vol. 19, no. 4, p. 875-898
Ajouter à la liste personnelle- Summary
- 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