Seminar - Takis Konstantopoulos

Speaker

Takis Konstantopoulos, Department of Mathematics, Uppsala University, Sweden

Topic

On the Extendibility of Finitely Exchangeable Probability Measures

Abstract

We give necessary and sufficient conditions in order that a finite sequence
of exchangeable random variables in a fairly general state space be
extendible to a longer finite or to an infinite exchangeable sequence. This is done by formulating the extendibility problem as the extension problem for certain bounded linear functionals on suitable normed spaces and by using the Hahn-Banach theorem and other functional measure-theoretic
techniques. We examine when such a finitely exchangeable random
sequence is a mixture (with respect to a probability measure) of product
measures and also study the preservation of the extendibility property
under suitable limiting operations.

Invited by Professor Andrew Heunis