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 ?
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.
We prove that for every measurable set A of finite Lebesgue measure,
n] a measurable set, f, g : [OMEGA] [right arrow] H Bochner measurable functions on [OMEGA] and f, g [member of] [L.
n] a measurable set and [rho] : [OMEGA] [right arrow] [0, [infinity]) a Lebesgue integrable function with [[integral].
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.
We intend the result to be a specific, measurable set of guidelines that will allow firms to 'self-audit' the objectivity of their research environment and report publicly whether they are in compliance with the highest standards in the industry.
This reward comes in measurable sets of results such as looking thinner and firmer, avoiding disease and living longer and feeling better emotionally.
We construct fuzzy number valued outer measures and measurable sets that is similar to that of Carathrodory construction.