Linear Operators: General theory |
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Page 171
... Suppose that every continuous function is u - measurable . Show that * contains every Borel set . 24 Suppose that S is a compact topological space , with the property that for every covering of S by a finite number of open sets . G1 ...
... Suppose that every continuous function is u - measurable . Show that * contains every Borel set . 24 Suppose that S is a compact topological space , with the property that for every covering of S by a finite number of open sets . G1 ...
Page 225
... suppose that B consists of a finite collection of disjoint closed rectifiable Jordan curves ; that is , we suppose that B can be decomposed into the union B B1UB2 U ... ○ B1 of dis- joint closed sets B , in such a way that each B , is ...
... suppose that B consists of a finite collection of disjoint closed rectifiable Jordan curves ; that is , we suppose that B can be decomposed into the union B B1UB2 U ... ○ B1 of dis- joint closed sets B , in such a way that each B , is ...
Page 360
... Suppose that 0≤ x ≤27 ( i ) ( Snf ) ( x ) → f ( x ) uniformly in a for f in AC . ( ii ) The convergence of Sf is localized . Show that for any ƒ in CBV , ( Sf ) ( a ) f ( x ) uniformly in a . - > 24 Suppose ( i ) , ( ii ) of the last ...
... Suppose that 0≤ x ≤27 ( i ) ( Snf ) ( x ) → f ( x ) uniformly in a for f in AC . ( ii ) The convergence of Sf is localized . Show that for any ƒ in CBV , ( Sf ) ( a ) f ( x ) uniformly in a . - > 24 Suppose ( i ) , ( ii ) of the last ...
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