outer measure


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outer measure

[′au̇d·ər ′mezh·ər]
(mathematics)
A function with the same properties as a measure except that it is only countably subadditive rather than countably additive; usually defined on the collection of all subsets of a given set.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
In Section 2 we study the set function [micro]p and prove that it should be viewed as an outer measure, rather than as a fuzzy measure.
It is clear that the integral representation (1.5) still holds, where [micro]p is viewed either as an outer measure, or as a capacity.
There are articles in the literature associated with fuzzy outer measure [3].
The fuzzy number valued Lebesgue outer measure for the fuzzy subset [mu] is defined as m*([mu]) = (0, [??]) where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and the infimum is taken over all countable collection ([I.sub.n]) of open intervals covering R.
The fuzzy number valued outer measure for the fuzzy subset [mu] is defined as m*([mu]) = (0, [??]) where K = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and the infimum is taken over all countable collection ([A.sub.n]) in [Omega] which cover X.
The text begins by introducing abstract concepts of measure and integration, such as basic set classes, outer measures, measure extension, and convergence of sequences.