Chapter

Weak Convergence in Metric Spaces

James Davidson

in Stochastic Limit Theory

Published in print October 1994 | ISBN: 9780198774037
Published online November 2003 | e-ISBN: 9780191596117 | DOI: http://dx.doi.org/10.1093/0198774036.003.0026

Series: Advanced Texts in Econometrics

 Weak Convergence in Metric Spaces

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This chapter lays the foundations for functional limit theory by considering the case of general metric spaces, from a topological standpoint. It develops tools to replace the method of characteristic functions and the inversion theorem, used for real sequences. Weak convergence of probability measures and the technique of metrizing the space of measures are considered. The concept of uniform tightness of a family of measures is introduced, and also the general form of Skorokhod's representation theorem.

Keywords: convergence determining class; measure space; metric space; metrization; regular measure; Skorokhod's representation theorem; tightness; weak convergence

Chapter.  13277 words.  Illustrated.

Subjects: Econometrics and Mathematical Economics

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