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Page 161
... ba ( S , E , X ) is complete . It follows , therefore , that ba ( S , E , X ) is a B - space . If is the set of real or complex numbers , then according to Lemma 1.5 , sup | μ ( E ) | ≤ v ( μ , S ) ≤ 4 sup | μ ( E ) \ . ΕΕΣ ΕΕΣ This ...
... ba ( S , E , X ) is complete . It follows , therefore , that ba ( S , E , X ) is a B - space . If is the set of real or complex numbers , then according to Lemma 1.5 , sup | μ ( E ) | ≤ v ( μ , S ) ≤ 4 sup | μ ( E ) \ . ΕΕΣ ΕΕΣ This ...
Page 311
... ba ( S , E ) . 9 THEOREM . The space ba ( S , Σ ) is weakly complete . If S is a topological space , the rba ( S ) is also weakly complete . PROOF . Consider the closed subspace B ( S , 2 ) of B ( S ) . According to Theorems 6.18 and ...
... ba ( S , E ) . 9 THEOREM . The space ba ( S , Σ ) is weakly complete . If S is a topological space , the rba ( S ) is also weakly complete . PROOF . Consider the closed subspace B ( S , 2 ) of B ( S ) . According to Theorems 6.18 and ...
Page 340
... S be a compact Hausdorff space . Show that C ( S ) is weakly complete if and only if it is finite dimensional ... ba ( S , Σ ) converge weakly to an element λ € ba ( S , 2 ) if and only if there exists a non- negative μ e ba ( S , Σ ) ...
... S be a compact Hausdorff space . Show that C ( S ) is weakly complete if and only if it is finite dimensional ... ba ( S , Σ ) converge weakly to an element λ € ba ( S , 2 ) if and only if there exists a non- negative μ e ba ( S , Σ ) ...
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