Sentence examples for measurable sets of from inspiring English sources

Under this assumption there is an increasing sequence of measurable sets of finite measure whose union equals Ω.

Using some previous results proved in collaboration with Hayman and Weitsman [84], he showed that there exists a constant C(n) such that for all measurable sets of finite measure begin{aligned} alpha (E ^4 le C(n) D(E).

Consider Ω = [ − 2, 5 ] and let β be a σ-algebra of Lebesgue measurable sets of [ − 2, 5 ].

Let Ω = R. β be a σ-algebra of Lebesgue measurable sets of ℝ. Define T : Ω × X → X by T ( ω, x ) = 1 3.

Soon it was shown using the Axiom of Choice that there are non-Lebesgue measurable sets of reals (Vitali, 1905), and also uncountable sets of reals with no perfect subset (Bernstein, 1908).

We recall that the total variation measure of any signed measure (mu ) is defined by begin{aligned} |mu |(mathcal{U }) mathop limits ^{mathrm{def}}sup sum _{i=1}^infty |mu (U_i)|, quad mathcal{U }subset mathbb T ^q!, end{aligned}where the supremum is taken over all countable partitions ({U_i}) into measurable sets of (mathcal{U }).

(v) We shall say that a measure is purely atomic if every measurable set of positive measure contains an atom.  .

If we have that there exists a measurable set of measure zero such that (2.16).

We say that nearly converges to with respect to as if for every there exists a measurable set, of measure less than such that (2.12).

We consider however, two fuzzy numbers to be equivalent if there exists a measurable set of measure zero such that (2.16) hold and if we do not distinguish between equivalent of fuzzy numbers then becomes a metric space with metric.

If μ is a measure on (mathbb{R}), and if (mathcal{S}subseteq mathbb{R}) is a measurable set of positive measure, then the integral mean point c=frac{1}{mu(mathcal{S})}int_{mathcal{S}}x,dmu (4) is called the barycenter of the set (mathcal{S}) respecting measure μ, or just the set barycenter.