Linear Operators: General theory |
From inside the book
Results 1-3 of 79
Page xvi
... sets are the same if and only if they have the same elements , i.e. , A = B if and only if ACB and BC A. The set A ... disjoint if their intersection is void . A family of sets is a disjoint family if every pair of distinct sets in the ...
... sets are the same if and only if they have the same elements , i.e. , A = B if and only if ACB and BC A. The set A ... disjoint if their intersection is void . A family of sets is a disjoint family if every pair of distinct sets in the ...
Page 2
... sets are the same if and only if they have the same elements , i.e. , A = B if and only if ACB and BCA . The set A ... disjoint if their intersection is void . A family of sets is a disjoint family if every pair of distinct sets in the ...
... sets are the same if and only if they have the same elements , i.e. , A = B if and only if ACB and BCA . The set A ... disjoint if their intersection is void . A family of sets is a disjoint family if every pair of distinct sets in the ...
Page 97
... set S. Then for every E in Σ the total variation of μ on E , denoted by v ( u , E ) , is defined as n v ( u , E ) = sup Σ | μ ( E ; ) \ , i = 1 where the supremum is taken over all finite sequences { E } of disjoint sets in with E , CE .
... set S. Then for every E in Σ the total variation of μ on E , denoted by v ( u , E ) , is defined as n v ( u , E ) = sup Σ | μ ( E ; ) \ , i = 1 where the supremum is taken over all finite sequences { E } of disjoint sets in with E , CE .
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