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Page 182
... defined u - almost everywhere by the formula 2 ( E ) = √ E Γαλ ( s ) } μ ( ds ) , ΕΕΣ . We close this section with ... defined on S2 is μ2 - measurable , then f ( $ ( · ) ) is μ - measurable ; ( e ) if μ is non - negative and countably ...
... defined u - almost everywhere by the formula 2 ( E ) = √ E Γαλ ( s ) } μ ( ds ) , ΕΕΣ . We close this section with ... defined on S2 is μ2 - measurable , then f ( $ ( · ) ) 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 μ is the total variation of μ on S , i.e. , | μ | = v ( μ , S ) . 16. The space ca ( S , E ) is defined for a σ ...
... defined for a field Σ of subsets of a set S and consists of all bounded additive scalar functions defined on 2. The norm μ is the total variation of μ on S , i.e. , | μ | = v ( μ , S ) . 16. The space ca ( S , E ) is defined for a σ ...
Page 516
... defined on the family of subsets of S is said to be 4 - in- variant in case μ ( E ) = u ( p - 1E ) , ECS , where 4 - 1E = [ sos € E ] . Show that there is a non - negative bounded additive function u defined for all subsets of S which ...
... defined on the family of subsets of S is said to be 4 - in- variant in case μ ( E ) = u ( p - 1E ) , ECS , where 4 - 1E = [ sos € E ] . Show that there is a non - negative bounded additive function u defined for all subsets of S which ...
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