On Central Limit Theorems in Probability Gage Spaces

Abstract

Some limit theorems in probability gage spaces over semifinite W*-algebras are proved In particular, a Levy-Khinchine type of representation for the Fourier transforms of limit probability gages is established. The results are obtained by exploiting some of the algebraic and topological properties of certain sets of operators, called the decomposability algebraic structures, associated with probability gages. This work has a number of points of contact with aspects of (Euclidean) Quantum Field Theory.