Linear Operators: General theory |
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Page 22
... finite number of a „ . Since a finite number of these neighborhoods cover A , the sequence { a } consists of only a finite number of distinct points of A , and there- fore most certainly does have a convergent subsequence . This contra ...
... finite number of a „ . Since a finite number of these neighborhoods cover A , the sequence { a } consists of only a finite number of distinct points of A , and there- fore most certainly does have a convergent subsequence . This contra ...
Page 200
... finite number of a , μ is non - negative and Ma ( Sa ) 1. In this case the product IIμ ( E ... ) is meaningful for the αελ type of set P E mentioned above , since E αελ α α α S and hence ( S ̧ ) = 1 α for all but a finite number of x ...
... finite number of a , μ is non - negative and Ma ( Sa ) 1. In this case the product IIμ ( E ... ) is meaningful for the αελ type of set P E mentioned above , since E αελ α α α S and hence ( S ̧ ) = 1 α for all but a finite number of x ...
Page 849
... finite , III.4.3 ( 126 ) Lebesgue extension of , III.5.18 ( 143 ) as a metric space , III.7.1 ( 158 ) , III.9.6 ( 169 ) positive , III.4.3 ( 126 ) product , of finite number of finite measure spaces , III.11.3 ( 186 ) of finite number of o ...
... finite , III.4.3 ( 126 ) Lebesgue extension of , III.5.18 ( 143 ) as a metric space , III.7.1 ( 158 ) , III.9.6 ( 169 ) positive , III.4.3 ( 126 ) product , of finite number of finite measure spaces , III.11.3 ( 186 ) of finite number of o ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ