Linear Operators: General theory |
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Page 145
... uniformly on S - E . The sequence { f } converges u - uniformly to the function f if for each & > 0 there is a set E e Σ such that v ( u , E ) < ɛ and such that { n } converges uniformly to ƒ on S - E . It is clear that u - uniform ...
... uniformly on S - E . The sequence { f } converges u - uniformly to the function f if for each & > 0 there is a set E e Σ such that v ( u , E ) < ɛ and such that { n } converges uniformly to ƒ on S - E . It is clear that u - uniform ...
Page 314
... uniformly for 22 € VK . It is then clear that μ V - 1 ( μ2 ) is a non - nega- tive element of ba ( S , E ) such that lim 2 ( E ) = 0 uniformly for λ € K . μ ( E ) → 0 To prove the converse , suppose there exists a non - negative μ e ba ...
... uniformly for 22 € VK . It is then clear that μ V - 1 ( μ2 ) is a non - nega- tive element of ba ( S , E ) such that lim 2 ( E ) = 0 uniformly for λ € K . μ ( E ) → 0 To prove the converse , suppose there exists a non - negative μ e ba ...
Page 360
... uniformly for a in some neighborhood of p . 21 Show that if fő En ( x , z ) dz | ≤ M , then the convergence of Snf for a given c.o.n. system is localized if and only if max | E , ( x , y ) | ≤M , < ∞ for each ɛ > 0 . 8 | xv | ≥ € 22 ...
... uniformly for a in some neighborhood of p . 21 Show that if fő En ( x , z ) dz | ≤ M , then the convergence of Snf for a given c.o.n. system is localized if and only if max | E , ( x , y ) | ≤M , < ∞ for each ɛ > 0 . 8 | xv | ≥ € 22 ...
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