Linear Operators: General theory |
From inside the book
Results 1-3 of 76
Page 132
... countably additive measures is μ - continuous and if lim , λ ( E ) = 2 ( E ) , EeΣ , where 2 is also a finite , countably additive measure , then 2 is also u - continuous . It follows easily from Definition 12 that if 2 , λn , n = 1 , 2 ...
... countably additive measures is μ - continuous and if lim , λ ( E ) = 2 ( E ) , EeΣ , where 2 is also a finite , countably additive measure , then 2 is also u - 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 Σ has a countably additive non - negative extension to the o - field determined by E. 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 Σ has a countably additive non - negative extension to the o - field determined by E. If μ is o - finite on then this extension is unique . PROOF ...
Page 405
... countably additive ; the subset l2 of s is of μ - measure zero ; the measure μ is not countably additive . In fact , using the relation between and μ , it is easy to see that l is the union of a countable family of u - null sets . These ...
... countably additive ; the subset l2 of s is of μ - measure zero ; the measure μ is not countably additive . In fact , using the relation between and μ , it is easy to see that l is the union of a countable family of u - null sets . These ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
59 other sections not shown
Other editions - View all
Common terms and phrases
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