Neveu J. Mathematical Foundations of the Calculus of Probability

San Francisco: Holden-day, 1965. - 235p.In its present state, the calculus of probability and, in particular, the theory of stochastic processes and vector-valued random variables, cannot
be understood by one who does not have, to begin with, a thorough understanding of measure theory. If one is to prepare for participation in the future development of thec alculus of probability, it is not sufficient to know the fundamental concepts and results of measure theory; one must also be experienced in its techniques and able t~hem and extend them to new situations.
Again, one often hears-and quite justifiably in a certain sense-that the calculus of probability is simply a paragraph of the theory of measure; but within measure theory, the calculus of probability stands out by the nature of the guestions which it seeks to answer- a nature which has its origins not in measure theory itself, but in the philosophical and practical content of the notion of probability.
The advanced course in the calculus of probability is aimed at those students having the body of knowledge which in France is called "licence de Mathematiques"; this body of knowledge covers mathematics in general. It naturally encompasses the theory of measure and integration, but is necessarily limited to an introduction to the subject. It is thus necessary that this question be taken up again and developed in advanced studies; it is still more necessary that its exposition be oriented specifically toward applications to probability theory.