Probabilistic Foundations

In the first chapter, Kolmogorov’s axioms of the theory of probability are presented. The choice of the system of the axioms is explained in context of the Caratheodory theorem. Different probability spaces as well as probability distributions are introduced too. The famous Kolmogorov consistency theorem is formulated, and as a consequence, a brief construction of the Wiener measure is shown (see [1], [6], [7], [10], [15], [19], [40], and [45]).