Linear Operators: General theory |
From inside the book
Results 1-3 of 63
Page 136
... 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 subsets of S , which contains a given family 7. The intersection of all fields ...
... 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 subsets of S , which contains a given family 7. The intersection of all fields ...
Page 166
... field , then Σ ( E ) is a σ - field . ( E ) is called the restriction of Σ to E. If Σ is a field , E € Σ1 , and Σ is the o - field generated by 21 , then we can easily show that Σ ( E ) is the o - field generated by E1 ( E ) . Indeed ...
... field , then Σ ( E ) is a σ - field . ( E ) is called the restriction of Σ to E. If Σ is a field , E € Σ1 , and Σ is the o - field generated by 21 , then we can easily show that Σ ( E ) is the o - field generated by E1 ( E ) . Indeed ...
Page 201
... field , is the o - field 2. An elementary set in S is one of the form Pac4 E where E is in E , and , for all but a finite number of x , E = S. Equivalently , an elementary set in S is one having the form SXE for some л and some E , in ...
... field , is the o - field 2. An elementary set in S is one of the form Pac4 E where E is in E , and , for all but a finite number of x , E = S. Equivalently , an elementary set in S is one having the form SXE for some л and some E , in ...
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