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Page 164
... non - negative set function on Σ to 21 is non - negative , it follows that { u , ( E ) } is a bounded non - decreasing set of real numbers for each E e Σ1 . We define λ ( E ) = lim ( E ) , E e E1 . By Corollary 4 , 21 is countably ...
... non - negative set function on Σ to 21 is non - negative , it follows that { u , ( E ) } is a bounded non - decreasing set of real numbers for each E e Σ1 . We define λ ( E ) = lim ( E ) , E e E1 . By Corollary 4 , 21 is countably ...
Page 179
... non- negative u - measurable function defined on S and λ ( E ) = √ ̧ f ( s ) μ ( ds ) , ΕΕΣ . Let g be a non - negative 2 - measurable function defined on S. Then fg is u - measurable , and √2g ( s ) λ ( ds ) = { 2 † ( s ) g ( s ) μ ...
... non- negative u - measurable function defined on S and λ ( E ) = √ ̧ f ( s ) μ ( ds ) , ΕΕΣ . Let g be a non - negative 2 - measurable function defined on S. Then fg is u - measurable , and √2g ( s ) λ ( ds ) = { 2 † ( s ) g ( s ) μ ...
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 . s on S 40 Let S be a non - void set and G a family of functions to S. Suppose that 41 ( 42 ( s ) ...
... 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 . s on S 40 Let S be a non - void set and G a family of functions to S. Suppose that 41 ( 42 ( s ) ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ