Linear Operators: General theory |
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Page 143
... measure on Σ as well as for its extension on * should cause no confusion . The measure of Lebesgue in an interval [ a , b ] of real numbers may be defined as the Lebesgue extension of the Borel measure in [ a , b ] . The Lebesgue ...
... measure on Σ as well as for its extension on * should cause no confusion . The measure of Lebesgue in an interval [ a , b ] of real numbers may be defined as the Lebesgue extension of the Borel measure in [ a , b ] . The Lebesgue ...
Page 186
... measure with the desired properties . To prove the uniqueness of μ , we note that it follows in the same way that ... measure space ( S , Σ , μ ) constructed in Theorem 2 is called the product measure space of the measure spaces ( Sn ...
... measure with the desired properties . To prove the uniqueness of μ , we note that it follows in the same way that ... measure space ( S , Σ , μ ) constructed in Theorem 2 is called the product measure space of the measure spaces ( Sn ...
Page 405
... measure Mis countably additive ; the subset l1⁄2 of s is of μ - measure zero ; the measure μ is not countably additive . In fact , using the relation between Мое and it is easy to see that l2 is the union of a countable family of u ...
... measure Mis countably additive ; the subset l1⁄2 of s is of μ - measure zero ; the measure μ is not countably additive . In fact , using the relation between Мое and it is easy to see that l2 is the union of a countable family of u ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space 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 exists f₁ finite dimensional function defined function f g₁ 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-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ