This book will enable researchers and students of analysis to more easily understand research papers in which probabilistic methods are used to prove theorems of analysis, many of which have no other known proofs. The book assumes a course in measure and integration theory but requires little or no background in probability theory.

Karl Stromberg (Kansas State University)

Fourier transforms on Rd
Weak convergence in M1 (Rd)
Independende
Infinite series of random vectors
Normal distributions and central limits
Martingales
Projective limits and infinite products of probability measures
Brownian motions
Random Fourier series of continuous functions
Fourier coefficients of continuous functions