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 off 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 off 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 , E ) satisfies the two conditions and let μ1 € K , n = 1 , 2 , .. .. Using the measure 2 defined above we have functions fe L1 ...
... respect to ƒ in K ' and hence uniform with respect to μ in K. Conversely , suppose that the set KC ca ( S , E ) satisfies the two conditions and let μ1 € K , n = 1 , 2 , .. .. Using the measure 2 defined above we have functions fe 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
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