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 u in K. Conversely , suppose that the set KC ca ( S , E ) satisfies the two conditions and let μ ‚ € 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 u in K. Conversely , suppose that the set KC ca ( S , E ) satisfies the two conditions and let μ ‚ € 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 . ( iii ) lim 。 U2λ = 2 uniformly with respect to λ € K. = 20 Let Σ { E } be a countable field of subsets of a set S , and let 1 be the o - field generated by Σ . Let μ be a non - negative ...
... respect to which every in K is continuous . ( iii ) lim 。 U2λ = 2 uniformly with respect to λ € K. = 20 Let Σ { E } be a countable field of subsets of a set S , and let 1 be the o - field generated by Σ . Let μ be a non - negative ...
Contents
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
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 compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations Doklady Akad Duke Math E₁ elements ergodic exists extension f₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality 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 o-field 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 topological space u-integrable u-measurable u-null uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ