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 BUBU ... UB of dis- joint closed sets B ; in such a way that each B , is a ...
... 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 BUBU ... UB of dis- joint closed sets B ; in such a way that each B , is a ...
Page 360
... Suppose ( i ) , ( ii ) of the last exercise . Show that if f is in BV then ( Sf ) ( x ) → f ( x ) at each point a where ƒ is continuous . 25 Suppose that ( Sf ) ( x ) → ( 1/2 ) ( f ( x + ) + f ( x- ) ) for each step function f . Show ...
... Suppose ( i ) , ( ii ) of the last exercise . Show that if f is in BV then ( Sf ) ( x ) → f ( x ) at each point a where ƒ is continuous . 25 Suppose that ( Sf ) ( x ) → ( 1/2 ) ( f ( x + ) + f ( x- ) ) for each step function f . Show ...
Contents
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
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 compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations Doklady Akad Duke Math E₁ elements ergodic exists extension f₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality 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 o-field 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 theory topological space u-integrable u-measurable u-null uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ