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.

Lebesgue exterior measure

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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.

Optimization in a Fuzzy Environment

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.

On fuzzy number valued Lebesgue outer measure

The text begins by introducing abstract concepts of measure and integration, such as basic set classes, outer measures, measure extension, and convergence of sequences.