A new proof of Kelley's Theorem

Abstract

Kelley's Theorem is a purely combinatorial characterization of measure algebras. We first apply linear programming to exhibit the duality between measures and this characterization for finite algebras. Then we give a new proof of the Theorem using methods from nonstandard analysis. First some notation and definitions. B always denotes a Boolean algebra of the form (B,0,1,+,·, ) with the induced ordering . We sometimes write P and Q for + and ·, especially when the operations are infinitary. By a measure µ on a subalgebra A B