Linear Operators: General theory |
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Page 136
Nelson Dunford, Jacob T. Schwartz. 6 LEMMA . There is a uniquely determined smallest field and a uniquely determined smallest o - field containing a given family of sets . PROOF . There is at least one field , namely the field of all ...
Nelson Dunford, Jacob T. Schwartz. 6 LEMMA . There is a uniquely determined smallest field and a uniquely determined smallest o - field containing a given family of sets . PROOF . There is at least one field , namely the field of all ...
Page 143
... determined by a func- tion f of bounded variation on a finite or infinite interval is the Le- besgue extension of the Borel - Stieltjes measure determined by f . If u is either the Borel - Stieltjes or the Lebesgue - Stieltjes measure ...
... determined by a func- tion f of bounded variation on a finite or infinite interval is the Le- besgue extension of the Borel - Stieltjes measure determined by f . If u is either the Borel - Stieltjes or the Lebesgue - Stieltjes measure ...
Page 455
... determined by GE We can even assert that each continuous linear functional ƒ can be included in a denumerable self - determined set G of functionals . For , if ƒ is determined by the denumerable set G1 , let each functional in G1 be ...
... determined by GE We can even assert that each continuous linear functional ƒ can be included in a denumerable self - determined set G of functionals . For , if ƒ is determined by the denumerable set G1 , let each functional in G1 be ...
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