Title

Metrics Defined via Discrepancy Functions

Abstract

We introduce the notion of a discrepancy function, as an extended real-valued function that assigns to a pair (A,U) of sets a nonnegative extended real number ω(A,U), satisfying specific properties. The pairs (A,U) are certain pairs of sets such that Asubset of or equal toU, and for fixed A, the function ω takes on arbitrarily small nonnegative values as U varies. We present natural examples of discrepancy functions and show how they can be used to define traditional pseudo-metrics, quasimetrics and metrics on hyperspaces of topological spaces and measure spaces.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Discrepancy function; Hyperspace; Metric; Pseudo-metric; Quasimetric; Symmetric; Whitney map

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2007 Elsevier, All rights reserved.


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