Linear Operators: General theory |
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Page 182
... defined u - almost everywhere by the formula Jdi 2 ( E ) - ( s ) } μ ( ds ) , ΕΕΣ . We close this section with a ... defined on S2 is u - measurable , then f ( p ( ) ) is μ - measurable ; ( e ) if μ , is non - negative and countably ...
... defined u - almost everywhere by the formula Jdi 2 ( E ) - ( s ) } μ ( ds ) , ΕΕΣ . We close this section with a ... defined on S2 is u - measurable , then f ( p ( ) ) is μ - measurable ; ( e ) if μ , is non - negative and countably ...
Page 240
... defined for a field Σ of subsets of a set S and consists of all bounded additive scalar functions defined on 2. The norm is the total variation of u on S , i.e. , │u = v ( u , S ) . 16. The space ca ( S , E ) is defined for a σ - field ...
... defined for a field Σ of subsets of a set S and consists of all bounded additive scalar functions defined on 2. The norm is the total variation of u on S , i.e. , │u = v ( u , S ) . 16. The space ca ( S , E ) is defined for a σ - field ...
Page 241
Nelson Dunford, Jacob T. Schwartz. defined on the o - field B of all Borel sets in S. The norm [ u ] is the total variation vu , S ) . 18. The space L , ( S , E , μ ) is defined for any real number p , 1 ≤ p < ∞ , and any positive ...
Nelson Dunford, Jacob T. Schwartz. defined on the o - field B of all Borel sets in S. The norm [ u ] is the total variation vu , S ) . 18. The space L , ( S , E , μ ) is defined for any real number p , 1 ≤ p < ∞ , and any positive ...
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