A probability operator

Abstract

From Introduction: In probability theory it is often convenient to represent laws by characteristic functions, these being particularly suited to classical analysis. Trotter has suggest ted that probability laws can also be represented by probability operators. These operators are easily handled since they are continuous, and hence bounded, positive linear operators on a normed linear space. This representation arises because distribution functions and their complete convergence correspond to probability operators and their complete convergence. Hence the relations between distribution functions and probability operators will be discussed before the introduction of probability laws.