Linear Operators: General theory |
From inside the book
Results 1-3 of 82
Page 186
... measure u of Lemma 1 is countably additive on Ø . Consequently , the restriction of u to the o - field Σ generated ... positive measure spaces ( $ 1 , 21 , μ1 ) and ( S2 , 22 , 2 ) . For each E in Σ and 82 in S the set E ( 82 ) = { 81 81 ...
... measure u of Lemma 1 is countably additive on Ø . Consequently , the restriction of u to the o - field Σ generated ... positive measure spaces ( $ 1 , 21 , μ1 ) and ( S2 , 22 , 2 ) . For each E in Σ and 82 in S the set E ( 82 ) = { 81 81 ...
Page 212
... positive measure defined on the o - field of Borel sets of a compact metric space S. A set ACS is said to be covered in the sense of Vitali by a family F of closed sets if each FF has positive u - measure and there is a positive ...
... positive measure defined on the o - field of Borel sets of a compact metric space S. A set ACS is said to be covered in the sense of Vitali by a family F of closed sets if each FF has positive u - measure and there is a positive ...
Page 304
... positive measure space and let 1 ≤ p ≤ ∞o . Suppose f1 + f2 = -18 , where fi , gx are positive elements k = 1 in L „ ( S , Σ , μ ) . Then there are positive elements h ̧ in L ( S , Σ , μ ) , j = 1 , 2 , k * 1 , .. n , such that n な ...
... positive measure space and let 1 ≤ p ≤ ∞o . Suppose f1 + f2 = -18 , where fi , gx are positive elements k = 1 in L „ ( S , Σ , μ ) . Then there are positive elements h ̧ in L ( S , Σ , μ ) , j = 1 , 2 , k * 1 , .. n , such that n な ...
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