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Page 28
... exists a do e D , such that o ( 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 ) = p . PROOF . Let de D be such that c1 ...
... exists a do e D , such that o ( 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 ) = p . PROOF . Let de D be such that c1 ...
Page 362
... exists a complex - valued regular measure μ in C * with a1 = f2rn ( y ) μ ( dy ) if and only if fΣx__ x Amna¤n ( x ) dx < K , for all m≥ 1. Show that there exists an ƒ in L1 with an ( y ) f ( y ) dy if and only if in addition . to the ...
... exists a complex - valued regular measure μ in C * with a1 = f2rn ( y ) μ ( dy ) if and only if fΣx__ x Amna¤n ( x ) dx < K , for all m≥ 1. Show that there exists an ƒ in L1 with an ( y ) f ( y ) dy if and only if in addition . to the ...
Page 724
... exists for each e e Σ , and that m is an element of ca ( S , E ) satisfying m ( q - le ) = m ( e ) . Hint . Consider the space of all u - continuous elements of ca ( S , Σ ) . 32 ( Y. N. Dowker ) Let S , 2 , 9 , m be as in the preceding ...
... exists for each e e Σ , and that m is an element of ca ( S , E ) satisfying m ( q - le ) = m ( e ) . Hint . Consider the space of all u - continuous elements of ca ( S , Σ ) . 32 ( Y. N. Dowker ) Let S , 2 , 9 , m be as in the preceding ...
Contents
Preliminary Concepts | 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 ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element ergodic exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ