The Law of Large Numbers in a Metric Space with a Convex Combination Operation
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- 作者：Pedro Terán and Ilya Molchanov
- 关键词：Convexification ; decomposability ; Doss expectation ; law of large numbers ; random sets
- 刊名：Journal of Theoretical Probability
- 出版年：2006
- 出版时间：December, 2006
- 年：2006
- 卷：19
- 期：4
- 页码：875-898
- 全文大小：183 KB
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Probability Theory and Stochastic Processes
Statistics - 出版者：Springer Netherlands
- ISSN：1572-9230
文摘
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.