20.1. Additional technical results on weak convergence Given two metric spaces S1, S2 and a measurable function f : S1 → S2, suppose S1 is equipped with some probability measure P. This induces a probability measure on S2 which is denoted by Pf−1 and is defined by Pf−1(A) = P(f−1(A) for every measurable set A ⊂ S2. Then for any random variable X : S2 → R, its expectation EPf −1 [X] is equal to ...

Methods allowing the design of a synchronized sequential machine, working in the fundamental mode, and realizing the behaviour of any given finite automaton are studied from a theoretical point of view; the transformations of the initial flow table lead in a natural way to the definition and to the use of master-slave flip-flops. 1. Introduetion The aim of this paper is to give a theoretical ba...

Let S1 and S2 be Γ-semigroups. In this note, we determine when S1 and S2 are isomorphic if the power semigroup of S1 and the power semigroup of S2 are o-isomorphic.