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.
Recommended Citation
W. J. Charatonik and M. Insall, "Metrics Defined via Discrepancy Functions," Topology and its Applications, Elsevier, Jan 2007.
The definitive version is available at https://doi.org/10.1016/j.topol.2006.12.008
Department(s)
Mathematics and Statistics
Keywords and Phrases
Discrepancy function; Hyperspace; Metric; Pseudo-metric; Quasimetric; Symmetric; Whitney map
International Standard Serial Number (ISSN)
0166-8641
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2007 Elsevier, All rights reserved.
Publication Date
01 Jan 2007
