Quantum Probability (Probability and Mathematical Statistics) Gudder, Stanley P.

Quantum probability is a subtle blend of quantum mechanics and classical probability theory. Its important ideas can be traced to the pioneering work of Richard Feynman in his path integral formalism.Only recently have the concept and ideas of quantum probability been presented in a rigorous axiomatic framework, and this book provides a coherent and comprehensive exposition of this approach. It gives a unified treatment of operational statistics, generalized measure theory and the path integral formalism that can only be found in scattered research articles.The first two chapters survey the necessary background in quantum mechanics and probability theory and therefore the book is fairly self-contained, assuming only an elementary knowledge of linear operators in Hilbert space.

Well-written generalization of classical probability theory needed for several approaches to quantum mechanics, in particular those of operational statistics and of the path-integral formalism.
--AMERICAN MATHEMATICAL MONTHLY
I strongly recommend this book, especially to young researchers in mathematics, theoretical physics, and the philosophy of science who might wish to work in this exciting and rapidly developing field.
--AMERICAN SCIENTIST
The present book enriches the collection of books and papers on the mathematical background of quantum mechanics.
--MATHEMATICAL REVIEWS