1. ON THE EXTENDIBILITY OF FINITELY EXCHANGEABLE PROBABILITY MEASURES.
- Author
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KONSTANTOPOULOS, TAKIS and LINGLONG YUAN
- Subjects
- *
HAUSDORFF spaces , *COMPACT spaces (Topology) , *PERMUTATIONS , *SET functions - Abstract
A length-n random sequence X1, . . . , Xn in a space S is finitely exchangeable if its distribution is invariant under all n! permutations of coordinates. Given N >n, we study the extendibility problem: when is it the case that there is a length-N exchangeable random sequence Y1, . . . ,YN so that (Y1, . . . , Yn) has the same distribution as (X1, . . . , Xn)? In this paper, we give a necessary and sufficient condition so that, for given n and N, the extendibility problem admits a solution. This is done by employing functional-analytic and measure-theoretic arguments that take into account the symmetry. We also address the problem of infinite extendibility. Our results are valid when X1 has a regular distribution in a locally compact Hausdorff space S. We also revisit the problem of representation of the distribution of a finitely exchangeable sequence. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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