algebra of subsets
algebra of subsets
[¦al·jə·brə əv ′səb‚sets] (mathematics)
An algebra of subsets of a set S is a family of subsets of S that contains the null set, the complement (relative to S) of each of its members, and the union of any two of its members.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive
If F is an
algebra of subsets of a set Y and [mu]: F [right arrow] E a finitely additive measure then [mu] will be called exhaustive if for any disjoint sequence {[A.sub.n]} [subset] F, we have [mu]([A.sub.n]) [right arrow] 0 ([2]); exhaustive measures are called strongly bounded measures in [1]; for quasi-complete E, a finitely additive [mu] is exhaustive iff [mu](F) is relatively weakly compact in E- for Banach spaces, it is proved in [1] and it easily extends to quasi-complete locally convex spaces.
We shall assume X as a nonempty set, [Omega] denotes a [sigma]-
algebra of subsets of X and m denotes a positive measure on [Omega].
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