Linear Operators: General theory |
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Page 195
Nelson Dunford, Jacob T. Schwartz. with respect to one variable and then with respect to the other , or vice versa . Indeed , according to Tonelli's theorem , both these inte- grals are equal to the integral of ƒ with respect to the ...
Nelson Dunford, Jacob T. Schwartz. with respect to one variable and then with respect to the other , or vice versa . Indeed , according to Tonelli's theorem , both these inte- grals are equal to the integral of ƒ with respect to the ...
Page 306
... respect to ƒ in K ' and hence uniform with respect to μ in K. Conversely , suppose that the set KC ca ( S , Σ ) satisfies the two conditions and let μ2 € K , n = 1 , 2 , . . .. Using the measure λ defined above we have functions f € L1 ...
... respect to ƒ in K ' and hence uniform with respect to μ in K. Conversely , suppose that the set KC ca ( S , Σ ) satisfies the two conditions and let μ2 € K , n = 1 , 2 , . . .. Using the measure λ defined above we have functions f € L1 ...
Page 341
... respect to which every in K is continuous . μ ( iii ) lim , Uλ = 2 uniformly with respect to λe K. = 20 Let Σ { E } be a countable field of subsets of a set S , and let 1 be the o - field generated by E. Let μ be a non - negative finite ...
... respect to which every in K is continuous . μ ( iii ) lim , Uλ = 2 uniformly with respect to λe K. = 20 Let Σ { E } be a countable field of subsets of a set S , and let 1 be the o - field generated by E. Let μ be a non - negative finite ...
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 B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ