Linear Operators: General theory |
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Page 143
... Borel measure ) of the o - field of Borel sets in [ a , b ] . Similarly , the Lebesgue - Stieltjes measure determined by a func- tion f of bounded variation on a finite or infinite interval is the Le- besgue extension of the Borel ...
... Borel measure ) of the o - field of Borel sets in [ a , b ] . Similarly , the Lebesgue - Stieltjes measure determined by a func- tion f of bounded variation on a finite or infinite interval is the Le- besgue extension of the Borel ...
Page 643
... Borel subset of the plane . For each Borel subset E of the real line let y ( E ) = ( x × ẞ ) { P ( E ) } . We call y the convolution of a and ẞ and write γ = a * ß . It is clear that y is a Borel measure and a * ß = ß * a . Now let E ...
... Borel subset of the plane . For each Borel subset E of the real line let y ( E ) = ( x × ẞ ) { P ( E ) } . We call y the convolution of a and ẞ and write γ = a * ß . It is clear that y is a Borel measure and a * ß = ß * a . Now let E ...
Page 838
... Borel measure ( or Borel - Lebesgue measure ) , construction of , ( 139 ) III.13.8 ( 223 ) Borel - Stieltjes measure , ( 142 ) Bound , of an operator , II.3.5 ( 60 ) in a partially ordered set , I.2.3 ( 4 ) in the ( extended ) real ...
... Borel measure ( or Borel - Lebesgue measure ) , construction of , ( 139 ) III.13.8 ( 223 ) Borel - Stieltjes measure , ( 142 ) Bound , of an operator , II.3.5 ( 60 ) in a partially ordered set , I.2.3 ( 4 ) in the ( extended ) real ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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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