D. R. Axelrad 
Foundations of the Probabilistic Mechanics of Discrete Media [PDF ebook] 

This latest volume in the Foundations & Philosophy of Science & Technology series provides an account of probabilistic functional analysis and shows its applicability in the formulation of the behaviour of discrete media with the inclusion of microstructural effects. Although quantum mechanics have long been recognized as a stochastic theory, the introduction of probabilistic concepts and principles to classical mechanics has in general not been attempted. In this study the author takes the view that the significant field quantities of a discrete medium are random variables or functions of such variables. Hence the probabilistic mechanics of discrete media are based on the mathematical theory of probability and the axiomatics of measure theory.