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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 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 ...
Page 657
... determined new state y . Since y is uniquely determined by a and t , a function & on S to S is defined by the equa- tion y = ( x ) . The flow 4 is assumed to have the property that ( i ) t Pt ( $ s ( x ) ) = $ t + s ( x ) , for all ...
... determined new state y . Since y is uniquely determined by a and t , a function & on S to S is defined by the equa- tion y = ( x ) . The flow 4 is assumed to have the property that ( i ) t Pt ( $ s ( x ) ) = $ t + s ( x ) , for all ...
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 ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite 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 TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ