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Stochastic Limit TheoryAn Introduction for Econometricians$
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James Davidson

Print publication date: 1994

Print ISBN-13: 9780198774037

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198774036.001.0001

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Weak Convergence in Metric Spaces

Weak Convergence in Metric Spaces

(p.413) 26 Weak Convergence in Metric Spaces
Stochastic Limit Theory

James Davidson

Oxford University Press

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

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