Linear Operators: General theory |
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Page 132
... countably additive measures is μ - continuous and if lim , 2 ( E ) = 2 ( E ) , Ee , where λ is also a finite , countably additive measure , then λ is also μ - continuous . It follows easily from Definition 12 that if 2 , λn , n = 1 , 2 ...
... countably additive measures is μ - continuous and if lim , 2 ( E ) = 2 ( E ) , Ee , where λ is also a finite , countably additive measure , then λ is also μ - continuous . It follows easily from Definition 12 that if 2 , λn , n = 1 , 2 ...
Page 136
... countably additive non - neg- ative extended real valued set function μ on a field E has a countably additive non - negative extension to the o - field determined by Σ . If μ is o - finite on then this extension is unique . PROOF ...
... countably additive non - neg- ative extended real valued set function μ on a field E has a countably additive non - negative extension to the o - field determined by Σ . If μ is o - finite on then this extension is unique . PROOF ...
Page 405
... countably additive ; the subset ↳ of s is of μ - measure zero ; the measure μ is not countably additive . In fact , using the relation between Моо and it is easy to see that l is the union of a countable family of u - null sets . These ...
... countably additive ; the subset ↳ of s is of μ - measure zero ; the measure μ is not countably additive . In fact , using the relation between Моо and it is easy to see that l is the union of a countable family of u - null sets . These ...
Contents
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
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 compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations Doklady Akad Duke Math E₁ elements ergodic exists extension f₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality 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 o-field 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 theory topological space u-integrable u-measurable u-null uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ