The knob of the discord
For (S, Î£) a measurable space, let C1 and C2 and be convex, weak* closed sets of probability measures on Î£. We show that if C1 âˆª C2 satisfies the Lyapunov property, then there exists a set A âˆˆ Î£ such that minÎ¼1 âˆˆ C1 Î¼1(A) > maxÎ¼2 âˆˆ C2 (A). We give applications to Maxmin Expected Utility and to the core of a lower probability.
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