Linear Operators: General theory |
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Page 164
... non - negative set function on to Σ is non - negative , it follows that { μ , ( E ) } is a bounded non - decreasing set of real numbers for each E e 21 . We define λ ( E ) = lim , μn ( E ) , E e 21. By Corollary 4 , 21 is countably ...
... non - negative set function on to Σ is non - negative , it follows that { μ , ( E ) } is a bounded non - decreasing set of real numbers for each E e 21 . We define λ ( E ) = lim , μn ( E ) , E e 21. By Corollary 4 , 21 is countably ...
Page 179
... non- negative μ - measurable function defined on S and ¿ ( E ) = √ ̧ f ( s ) μ ( ds ) , E ΕΕΣ . Let g be a non - negative 2 - measurable function defined on S. Then fg is μ - measurable , and √gg ( s ) λ ( ds ) = √ ¿ f ( s ) g ( s ) ...
... non- negative μ - measurable function defined on S and ¿ ( E ) = √ ̧ f ( s ) μ ( ds ) , E ΕΕΣ . Let g be a non - negative 2 - measurable function defined on S. Then fg is μ - measurable , and √gg ( s ) λ ( ds ) = √ ¿ f ( s ) g ( s ) ...
Page 516
... non - negative measure μ defined for all Borel sets in S with the prop- erties that μ is not identically zero and u is p - invariant . 40 Let S be a non - void set and G a family of functions & on S to S. Suppose that 41 ( 42 ( 8 ) ...
... non - negative measure μ defined for all Borel sets in S with the prop- erties that μ is not identically zero and u is p - invariant . 40 Let S be a non - void set and G a family of functions & on S to S. Suppose that 41 ( 42 ( 8 ) ...
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