Distribution Functions and Characteristic Functions
In this chapter we introduce and discuss two important tools in the study of random variables, namely the distribution function and the characteristic function. Distribution functions of random variables encompass the probabilities of all events involving them, and characteristic functions associated to distribution functions, while paralleling their properties, are easy to handle by methods and results in classical analysis.
19 Distribution Functions
Given a probability space , a random variable is by definition an -measurable mapping from into . By (9.26), it induces the probability ...