For (S, Σ) a measurable space, let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\cal C}_1$$</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${\cal C}_2$$</EquationSource> </InlineEquation> be convex, weak<Superscript>*</Superscript> closed sets of probability measures on Σ. We show that if <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$${\cal C}_1$$</EquationSource> </InlineEquation> ∪ <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$${\cal C}_2$$</EquationSource> </InlineEquation> satisfies the Lyapunov property , then there exists a set A ∈ Σ such that min<Subscript>μ1</Subscript>∈<InlineEquation ID="IEq5"> <EquationSource...</equationsource></inlineequation></subscript></equationsource></inlineequation></equationsource></inlineequation></superscript></equationsource></inlineequation></equationsource></inlineequation>

For (S, S) a measurable space, let C1 and C2 and be convex, weak* closed sets of probability measures on S. We show that if C1 C2 satisfies the Lyapunov property, then there exists a set A S such that min C1 (A) max C2 (A). We give applications to Maxmin Expected Utility and to the core of a...

We study the cores of non-atomic market games, a class of transferable utility co- operative games introduced by Aumann and Shapley [2], and, more in general, of those games that admit a na-continuous and concave extension to the set of ideal coalitions, studied by Einy, Moreno, and Shitovitz...