Basic Concepts, Probability Inequalities and Limit Theorems

Let us, for later considerations, first introduce some common but important concepts of random variables (r.v.) and a corresponding limit theorem. First, explicit upper bounds on the deviation probability between r.v. averages, like \(\bar{\gamma }_{N_1,N_2}\) resp. \(\epsilon _{N_2}\) , and its corresponding mean are needed to establish in Chapter 3 and Chapter 4 the almost sure convergence results.