Scaled Boolean Algebras

Michael Hardy


October 20,
refreshments at 3:45pm


A problem in the foundations of probability inspired the definition of a "scale" -- a certain kind of increasing function whose domain is a Boolean algebra and whose range is a poset. A scale rho : A ---> S induces operations on S that make S behave in some ways like a Boolean algebra, satisfying a modular law and some de Morgan laws. In some other ways, S behaves quite unlike Boolean algebras -- in particular, in some cases S is not a lattice. Examples of scales will be exhibited, basic properties of scales will be proved, and their application to probability will be explained.

Speaker's Contact Info: hardy(at-sign)

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