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 ɛ > 0 there is a set E e Σ such that v ( μ , E ) < ɛ and such that { f } converges uniformly to f on S - E . It is clear that μ - uniform ...
... uniformly on S - E . The sequence { f } converges u - uniformly to the function f if for each ɛ > 0 there is a set E e Σ such that v ( μ , E ) < ɛ and such that { f } converges uniformly to f on S - E . It is clear that μ - uniform ...
Page 314
... uniformly for 29 € VK . It is then clear that u = V - 1 ( u ) is a non - nega- tive element of ba ( S , 2 ) such that lim 2 ( E ) = 0 uniformly for eK . 2 μ ( E ) - > 0 To prove the converse , suppose there exists a non - negative μ e ...
... uniformly for 29 € VK . It is then clear that u = V - 1 ( u ) is a non - nega- tive element of ba ( S , 2 ) such that lim 2 ( E ) = 0 uniformly for eK . 2 μ ( E ) - > 0 To prove the converse , suppose there exists a non - negative μ e ...
Page 360
... uniformly for a in some neighborhood of p . 21 Show that if fő En ( x , z ) dz ≤ M , then the convergence of Sf for a given c.o.n. system is localized if and only if max | E , ( x , y ) 1x - 12 € M. < ∞ for each ɛ > 0 . 8 22 Suppose ...
... uniformly for a in some neighborhood of p . 21 Show that if fő En ( x , z ) dz ≤ M , then the convergence of Sf for a given c.o.n. system is localized if and only if max | E , ( x , y ) 1x - 12 € M. < ∞ for each ɛ > 0 . 8 22 Suppose ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space 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 Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ