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Page 137
... field B containing all the closed sets of a given topological space S is called the Borel field of S , and the sets ... G in Σ whose interior contains E such that [ μ ( C ) | < ɛ for every C in with CCG - F . For a complex or extended real ...
... field B containing all the closed sets of a given topological space S is called the Borel field of S , and the sets ... G in Σ whose interior contains E such that [ μ ( C ) | < ɛ for every C in with CCG - F . For a complex or extended real ...
Page 143
... field . Now if EUN , EUN2 and NC M1 . No2 CM2 , let M = M1 ○ M2 so that E1 ○ M = E2 ○ M and thus μ ( E1 ) = μ ... g is u - integrable then the integral , g ( s ) u ( ds ) is often written g ( s ) dj ( s ) . In the case where f ( s ) ...
... field . Now if EUN , EUN2 and NC M1 . No2 CM2 , let M = M1 ○ M2 so that E1 ○ M = E2 ○ M and thus μ ( E1 ) = μ ... g is u - integrable then the integral , g ( s ) u ( ds ) is often written g ( s ) dj ( s ) . In the case where f ( s ) ...
Page 223
... g be a function defined on ( a , b ) such that the Lebesgue - Stieltjes integral I fag ( s ) dh ( s ) exists . Let ƒ ... field { -1 ( E ) E e Σ } is the G - field of Borel sets of I , and that if we put λ ( q ̄1 ( E ) ) = μ ( E ) , 2 is ...
... g be a function defined on ( a , b ) such that the Lebesgue - Stieltjes integral I fag ( s ) dh ( s ) exists . Let ƒ ... field { -1 ( E ) E e Σ } is the G - field of Borel sets of I , and that if we put λ ( q ̄1 ( E ) ) = μ ( E ) , 2 is ...
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