Chapter

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/10.1093/0198774036.003.0005

Series: Advanced Texts in Econometrics

 Metric Spaces

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This chapter introduces and illustrates the concept of a metric (distance measure), and the definition of a metric space. Open, closed, and compact sets are discussed in a general context, and the concepts of separability and completeness introduced. It goes on to look at mappings on metric spaces, and then examines the important case of function spaces, and treats the Arzelà‐Ascoli theorem.

Keywords: Arzelà‐Ascoli theorem; compact set; completeness; equicontinuity; Euclidean space; function space; metric; metric space; open set; separability

Chapter.  10053 words.  Illustrated.

Subjects: Econometrics and Mathematical Economics

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