Measurable Set

measurable set

[′mezh·rə·bəl ′set]
(mathematics)
A member of the sigma-algebra of subsets of a measurable space.

Measurable Set

 

(in the original meaning), a set to which the definition of measure given by the French mathematician H. Lebesgue is applicable. Measurable sets are one of the principal concepts of the theory of functions of a real variable and are the most important and an extremely broad class of point sets. In particular, closed sets and open sets lying on some segment are measurable sets. In the abstract theory of measure, sets belonging to the domain of definition μ are said to be measurable with respect to some measure μ. In the case when μ is a probability distribution, measurable sets are also called random events.

References in periodicals archive ?
x] = {y [member of] X : (x, y) [member of] X} contains at most continuum of distinct sets and consequently the diagonal D = {(x, x) : x [member of] X} is no longer a measurable set (see [2], p.
Y] (f (t))) + [epsilon]} is a measurable set in the product space.
Let G be a bounded measurable set, then meas(G+(8)) and meas(G"(8)) are continuous functions of 8.
You need a measurable set of variables to observe in order to show improvement over time.
However, defining legacy is problematic especially if conceived as an entirely predictable or measurable set of objectives.
For any [epsilon] [member of] (0,1) there exists a measurable set E [subset] [0,1], |E| > (1 - [epsilon]) and a series in the Walsh system {[[phi].
The object of study of this paper is the covariogram gA of a measurable set A [subset] [R.
n] a measurable set, f, g : [OMEGA] [right arrow] H Bochner measurable functions on [OMEGA] and f, g [member of] [L.
Rather, we want standards that are developed by a group of experts working on behalf of the entire food industry so that at the end of day what comes out is a consistent, science-based, measurable set of guidelines.
Broadwing's unified SLA provides a simple, consistent, and measurable set of performance guarantees that address the performance issues customers tell us are most meaningful to them.
A] denotes the characteristic function of the F measurable set A, then we use [[?