Linear Operators: General theory |
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Page 136
... unique . PROOF . Theorem 4 and Lemma 5 show that the outer measure μ is one non - negative countably additive extension of μ to the σ - field Zo determined by 2. Suppose that μ is another such extension . If μ is σ - finite on to prove ...
... unique . PROOF . Theorem 4 and Lemma 5 show that the outer measure μ is one non - negative countably additive extension of μ to the σ - field Zo determined by 2. Suppose that μ is another such extension . If μ is σ - finite on to prove ...
Page 202
... unique . This uniqueness argument suggests how we may prove the existence of u . For each finite set л in A there is , by Lemma 1 , a unique additive set function u , defined on has the property M2 ( PE ) - II “ a ( Ea ) , αεπ αεπ Let u ...
... unique . This uniqueness argument suggests how we may prove the existence of u . For each finite set л in A there is , by Lemma 1 , a unique additive set function u , defined on has the property M2 ( PE ) - II “ a ( Ea ) , αεπ αεπ Let u ...
Page 516
... unique up to a positive constant factor if and only if n - 1 ( p ( s ) ) converges uniformly to a constant for each ... unique regular measure u defined for the Borel subsets of S such that μ ( þ - 1 ( E ) ) = μ ( E ) for each Borel ...
... unique up to a positive constant factor if and only if n - 1 ( p ( s ) ) converges uniformly to a constant for each ... unique regular measure u defined for the Borel subsets of S such that μ ( þ - 1 ( E ) ) = μ ( E ) for each Borel ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ