# measurable space

## measurable space

[′mezh·rə·bəl ′spās]
(mathematics)
A set together with a sigma-algebra of subsets of this set.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Let ([OMEGA], [SIGMA]) be a measurable space and C be a nonempty closed convex sunset of a separable Banach space E.
Let [OMEGA] be a measurable space. Naturally, we say that an operator valued function f : [OMEGA] [right arrow] B(H) is [tau]-measurable provided that [f.sup.-1](O) is measurable for any open set O in the topology [tau].
We propose to partition the sample space according to their weak ergodic limit: assume a measurable space ([OMEGA], F), as above, and assume a surjective measurable function [theta] : ([OMEGA], F) [right arrow] ([OMEGA], F).
Let q(*) be a Poisson point process in a measurable space (Z, B(Z)) and induced compensating martingale measure [??](dt, dif) described on a complete probability space ([OMEGA], F, P).
Let (X, [OMEGA]) be a measurable space and [mu] and v be two measures on it.
Let [OMEGA] be a measurable space. An operator valued function f : [OMEGA] [right arrow] B(H) is called [tau]-measurable if [f.sup.-1] (O) is measurable for any arbitrary [tau]-open set O in B(H).
Let (X, F) be a measurable space, where X is a state space and F is [sigma]-algebra on X, and S(X, F) the set of all probability measures on (X, F).
By a measurable space, we shall mean as usually the pair ([OMEGA], [summation]), where the set [OMEGA] is equipped with a [sigma]-algebra [summation] of subsets.
The material is grouped by session, with individual paper topics that include model checking multivariate state rewards, a prediction model for software perfomance in symmetric multiprocessing environments, and the measurable space of stochastic processes.
Some terms: measurable space, probabilistic space, elementary event, the space of elementary events, sigma algebra, complex event, the function of probability, the probability of events, axioms of probability theory and Borel [sigma]-algebra as defined in (Sarapa, 1993).
Let (X, [OMEGA] )be a measurable space where [OMEGA] is a non-empty class of subsets of X.
Bonnefoy concludes that Masaccio used both metaphysical and measurable space and time.

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