Defining fractals in a probability space

Abstract

The Billingsley formulation (which we use) depends critically on a fixed stochastic process {X, X2,... taking values in a finite or countable state space S. No information about a subset E c f has any relevance unless it depends on the values {Xn(to)}. This means that we would lose nothing by assuming that f is an infinite product of a sequence of copies of S, which would make a typical point to (Xl, x2,..., xn,...), where each x S.