Sentence examples for be a separable metric from inspiring English sources

Let S be a separable metric space, (F Ttimes Wto2^{S}) a multifunction with nonempty values.

Let ((Omega,Sigma)) be a measurable space and Y be a separable metric space.

Let X be a separable metric space, Y a metric space and (f : Omegatimes Xto Y) a continuous random operator.

Let S be a separable metric space, and let (F Ttimes Xto2^{S}) be a multifunction with nonempty complete values.

Let ((Omega, Sigma)), Y be a separable metric space and (F: Omegato{mathcal{P}}_{cl}(Y)) be measurable multivalued.

Definition 4.2 Let Y be a separable metric space and let N Y Y → P L 1 0, 1, ℝ be a multivalued operator.

A mapping F : J ⊸ Y, where Y is a separable metric space, is called measurable if, for each open subset U ⊂ Y, the set { t ∈ J ∣ F ( t ) ⊂ U } belongs to a σ-algebra of subsets of J.

Since X is a separable metric space, there exists ({x_{i} : iin mathbb{N}} subseteq C) such that begin{aligned} &overline{{x_{i} : iin mathbb{N}}} = C, &G_^{-1}(C)=bigcap_{i=1}^{infty} bigcup_{n=1}^{infty} biggl{ omegainOmega: dbigl(x_{i},F omega,x_{i} bigr)< frac{1}{n} biggr}.

Let be a separable complete metric space and its Borel -field.

Let ((Omega, Sigma)), Y be a separable generalized metric space and (F: Omegato{mathcal{P}}_{cl}(Y)) be measurable multivalued.

Let X be a separable generalized metric space and (G: Omegatimes Xto X) be a mapping such that (G cdot,x)) is measurable for all (xin X) and (G omega,cdot)) is continuous for all (omega inOmega).