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Definition of Metric space

1. Noun. A set of points such that for every pair of points there is a nonnegative real number called their distance that is symmetric and satisfies the triangle inequality.

Definition of Metric space

1. Noun. (mathematics) Any space whose elements are points, and between any two of which a non-negative real number can be defined as the distance between the points; an example is Euclidean space ¹

¹ Source: wiktionary.com

Lexicographical Neighbors of Metric Space

Literary usage of Metric space

Below you will find example usage of this term as found in modern and/or classical literature:

1. Empirical Processes by Peter Gaenssler (1983)
"Weak convergence of non-BOREL measures on a metric space. Let S = (S,d) be a metric space with metric d and let B (S) = В (S,d) be the a-algebra in S ..."

2. Real Analysis by Andrew M. Bruckner, Judith B. Bruckner, Brian S. Thomson (1997)
"focus on essentials of the structure. 3.1 metric space Sequence limits in IR are denned using the metric p(x,y) = x - y\ (x ..."

3. Dynamics & Stochastics: Festschrift in Honour of M.S. Keane by Dee Denteneer, F. den Hollander, M. S. Keane, Evgeny Verbitskiy (2006)
"A continuous map / : X —• X of a compact metric space, with metric d, ... Every compact metric space that supports a continuous, one-to-one, ..."

4. Elementary Real Analysis by Brian S. Thomson, Judith B. Bruckner, Andrew M. Bruckner (2000)
"Theorem 13.65 A metric space (X, d) is complete if and only if the intersection ... You should also check the following useful version: A metric space (X, ..."

5. Oil Spill Dispersants: Efficacy And Effects by National Research Council (U. S.) (2005)
"... now that the set fl is a metric space, F is the Borel sigma algebra of ... if 1 is a compact metric space, then the set of all probability measures on ..."

6. Game Theory, Optimal Stopping, Probability and Statistics: Papers in Honor by Thomas Shelburne Ferguson, F. Thomas Bruss, Lucien Marie Le Cam (2000)
"This paper develops an extension of the classical kernel estimate of a multivariate density based on iid variables, to the metric space context using ..."

7. Selected Proceedings of the Sheffield Symposium on Applied Probability by Ishwar V. Basawa, Robert Lee Taylor (1991)
"For a locally compact complete separable metric space S, let M(S) denote the space of bounded Radon measures on 5, furnished with an appropriate metric so ..."

8. Invariant Measures on Groups and Their Use in Statistics by Robert A. Wijsman (1990)
"A metric space X with a distance function d is made into a topological space by taking as a base for the neighborhoods system of xGX the open balls ..."

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