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 ( μ , E ) < ɛ and such that { n } converges uniformly to f 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 ( μ , E ) < ɛ and such that { n } converges uniformly to f on S - E . It is clear that u - uniform ...
Page 314
... uniformly for 22 € VK . It is then clear that u tive element of ba ( S , E ) such that lim λ ( E ) μ ( E ) -0 = H2 ( E ) → 0 V - 1 ( μ2 ) is a non - nega- = 0 uniformly for λ € K . To prove the converse , suppose there exists a non ...
... uniformly for 22 € VK . It is then clear that u tive element of ba ( S , E ) such that lim λ ( E ) μ ( E ) -0 = H2 ( E ) → 0 V - 1 ( μ2 ) is a non - nega- = 0 uniformly for λ € K . To prove the converse , suppose there exists a non ...
Page 360
... uniformly for x in some neighborhood of p . 21 Show that if | ső E „ ( x , z ) dz | ≤M , then the convergence of ... uniformly for every f in AC . Show that there exists a finite constant K such that for f in CBV , | ( Snf ) ( x ) | ≤K ...
... uniformly for x in some neighborhood of p . 21 Show that if | ső E „ ( x , z ) dz | ≤M , then the convergence of ... uniformly for every f in AC . Show that there exists a finite constant K such that for f in CBV , | ( Snf ) ( x ) | ≤K ...
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 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