Robert Simon (London School of Economics) will give a talk on
Measure theoretic paradoxes as the only fixed points of a continuous operator
Abstract:
Given measure preserving transformations g_1 ….g_k on a probability space X and a set Y of colours a colouring rule is a correspondence F (a multi function) from X x Y^k to Y. A function f from X to Y satisfies the colouring rule if almost everywhere f(x) is in F(x, g_1x, …., g_kx). The rule is paradoxical if there is an f satisfying the rule but none that are measurable with respect to any finitely additive measure extending the probability measure and for which the g_i remain measure preserving. We show that usc convex valued correspondences can be paradoxical.