Linear Operators: General theory |
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Page 164
... non - negative set function on to 21 is non - negative , it follows that { ( E ) } is a bounded non - decreasing set of real numbers for each E e 21 . We define λ ( E ) = lim , μ „ ( E ) , E € 21. By Corollary 4 , 21 is countably ...
... non - negative set function on to 21 is non - negative , it follows that { ( E ) } is a bounded non - decreasing set of real numbers for each E e 21 . We define λ ( E ) = lim , μ „ ( E ) , E € 21. By Corollary 4 , 21 is countably ...
Page 179
... non- negative u - measurable function defined on S and λ ( E ) = √2 † ( s ) μ ( ds ) , E ΕΕΣ . Let g be a non - negative 2 - measurable function defined on S. Then fg is u - measurable , and √2g ( s ) 2 ( ds ) = √2f ( $ ) g ( s ) μ ...
... non- negative u - measurable function defined on S and λ ( E ) = √2 † ( s ) μ ( ds ) , E ΕΕΣ . Let g be a non - negative 2 - measurable function defined on S. Then fg is u - measurable , and √2g ( s ) 2 ( ds ) = √2f ( $ ) g ( s ) μ ...
Page 516
... not identically zero and is p - invariant . 39 Let S be a compact Hausdorff space and a continuous function on S to S. Show that there is a regular countably additive non - negative measure u defined for all Borel sets in S with the ...
... not identically zero and is p - invariant . 39 Let S be a compact Hausdorff space and a continuous function on S to S. Show that there is a regular countably additive non - negative measure u defined for all Borel sets in S with the ...
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 B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ