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Page 28
... exists a do e D , such that g ( f ( p ) , f ( q ) ) < ɛ if p≥ do , q≥ do . 5 LEMMA . If f is a generalized Cauchy sequence in a complete metric space X , there exists a pe X such that lim f ( d ) n = p . PROOF . Let de D be such that ...
... exists a do e D , such that g ( f ( p ) , f ( q ) ) < ɛ if p≥ do , q≥ do . 5 LEMMA . If f is a generalized Cauchy sequence in a complete metric space X , there exists a pe X such that lim f ( d ) n = p . PROOF . Let de D be such that ...
Page 292
... exists for E e Σ1 . Then lim ( E ) exists for E e 2 . ∞48 PROOF . Let be the family of all sets E in E for which lim u , ( EF ) exists for each Fe 21 , and let 23 be the family of all sets E 321400 1 2 Ε 1 1 in E for which EF € 22 for ...
... exists for E e Σ1 . Then lim ( E ) exists for E e 2 . ∞48 PROOF . Let be the family of all sets E in E for which lim u , ( EF ) exists for each Fe 21 , and let 23 be the family of all sets E 321400 1 2 Ε 1 1 in E for which EF € 22 for ...
Page 362
... exists a complex - valued regular measure u in C * with an if and only if Σx__ ∞ λmnan ‡ n ( x ) | dx < K , for all m ≥ 1. Show that there exists an ƒ in L1 with a , = f ( y ) f ( y ) dy if and only if in addition to the preceding ...
... exists a complex - valued regular measure u in C * with an if and only if Σx__ ∞ λmnan ‡ n ( x ) | dx < K , for all m ≥ 1. Show that there exists an ƒ in L1 with a , = f ( y ) f ( y ) dy if and only if in addition to the preceding ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz 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