Linear Operators: General theory |
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Page 136
... unique . PROOF . Theorem 4 and Lemma 5 show that the outer measure û is one non - negative countably additive extension of μ to the o - field E determined by 2. Suppose that μ1 is another such extension . If is o - finite on Σ to prove ...
... unique . PROOF . Theorem 4 and Lemma 5 show that the outer measure û is one non - negative countably additive extension of μ to the o - field E determined by 2. Suppose that μ1 is another such extension . If is o - finite on Σ to prove ...
Page 202
... unique . This uniqueness argument suggests how we may prove the existence of μ . For each finite set л in A there is , by Lemma 1 , a unique additive set function μ defined on Σ , which has the property = ( PE ) II Ma ( Ea ) , Π аел αεπ ...
... unique . This uniqueness argument suggests how we may prove the existence of μ . For each finite set л in A there is , by Lemma 1 , a unique additive set function μ defined on Σ , which has the property = ( PE ) II Ma ( Ea ) , Π аел αεπ ...
Page 516
... unique up to a positive constant factor if and only if n - 1 Σf ( ' ( s ) ) converges uniformly to a constant for each fe B ( S ) . n - 1 i = 0 43 Show that in Exercise 39 the measure μ is unique up to a positive constant factor if and ...
... unique up to a positive constant factor if and only if n - 1 Σf ( ' ( s ) ) converges uniformly to a constant for each fe B ( S ) . n - 1 i = 0 43 Show that in Exercise 39 the measure μ is unique up to a positive constant factor if and ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ