Measures on Metric Spaces

Abstract

Abstract This chapter lays the foundations for functional limit theory, considering the case of general metric spaces from a topological standpoint. The issues of separability and measurability and techniques for assigning measures in metric spaces are then discussed, developing tools to replace the methods of characteristic functions and the inversion theorem used for real sequences. The key cases of function spaces are studied and in particular the case C of continuous functions on the unit interval. Weiner measure (Brownian motion) is defined as the leading case of a measure on C.