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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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Metric Spaces

Metric Spaces

Chapter:
(p.75) 5 Metric Spaces
Source:
Stochastic Limit Theory
Author(s):

James Davidson

Publisher:
Oxford University Press
DOI:10.1093/0198774036.003.0005

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

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