Algebraic Probability Theory

This monograph on the application of algebraic methods to probability theory uses topological algebraic manipulations to develop a general theory of the decomposition of distributions of random variables, which eliminates probability from the most fundamental theorems of probability theory. The book includes developing new theories and a summary of important existing results in the field. The final chapter describes a number of other applications of algebraic methods to probability theory, and a list of unsolved problems in the field.