Sentence examples for be a complete finite from inspiring English sources

Let ( Ω, F, μ ) be a complete finite separable measure space, and let Y be a separable Banach space.

Let now ( Ω, F, μ ) be a complete, finite measure space, and Y be a topological space.

Let ( Ω, F, μ ) be a complete, finite measure space, and let Y be a complete separable metric space.

Theorem 3 Let ( Ω, F, μ ) be a complete finite separable measure space, and let Y be a separable Banach space.

If | I | = 1, we obtain the following corollary of Theorem 2. Corollary 1 Let ( Ω, F, μ ) be a complete finite separable measure space, and let Y be a separable Banach space.

Let ( Ω, F, μ ) be a complete finite measure space, let Y be a separable Banach space, and let T : Ω → 2 Y be an integrably bounded, convex, weakly compact and a nonempty valued correspondence.

What makes The Americans an ideal subject for study is that it is a complete, finite piece of work.

Since ( Ω, F, μ ) is a complete finite measure space, Y is a separable Banach space, and X i : Ω → 2 Y has a measurable graph, by Aumann's selection theorem (see Appendix), it follows that there exists a F i -measurable function f i : Ω → Y such that f i ∈ X i μ-a.e.

Throughout this article, let ( Ω, A, μ ) be a complete σ-finite measure space and X be a separable real Banach space endowed with dual space X*, the norm ∥.∥ and the dual pair 〈.,.〉 between X and X*.

Theorem 1.2 Let ( M, F, d μ ) be a complete noncompact Finsler n-manifold with finite reversibility λ.

Throughout this paper, let be a complete -finite measure space and be a separable real Banach space.