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.
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].
Assume that these beliefs are represented by a probability measure on an algebra of subsets of S.