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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 GF . We can even assert that each continuous linear functional ƒ can be included in a denumerable self - determined set G of functionals . For , if f is determined by the denumerable set G1 , let each functional in G1 be ...
... determined by GF . We can even assert that each continuous linear functional ƒ can be included in a denumerable self - determined set G of functionals . For , if f 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 4 , on S to S is defined by the equa- tion y ( x ) . The flow o , is assumed to have the property that ( i ) $ t ( $ s ( x ) ) = $ t + s ( X ) , for all ...
... determined new state y . Since y is uniquely determined by a and t , a function 4 , on S to S is defined by the equa- tion y ( x ) . The flow o , is assumed to have the property that ( i ) $ t ( $ s ( x ) ) = $ t + s ( X ) , for all ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element ergodic exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f 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 S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ