Linear Operators: General theory |
From inside the book
Results 1-3 of 84
Page 136
... unique . μ PROOF . Theorem 4 and Lemma 5 show that the outer measure μ is one non - negative countably additive extension of μ to the o - field Zo determined by 2. Suppose that is another such extension . If μ is o - finite on to prove ...
... unique . μ PROOF . Theorem 4 and Lemma 5 show that the outer measure μ is one non - negative countably additive extension of μ to the o - field Zo determined by 2. Suppose that is another such extension . If μ is o - finite on 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 ) , 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 ) , аел αεπ ...
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 ( p - 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 ( p - 1 ( E ) ) = μ ( E ) for each Borel ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
31 other sections not shown
Other editions - View all
Common terms and phrases
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 continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional 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 Russian 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