## Linear Operators: General theory |

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a - 23

**Suppose**that S is a metric space , that is a o - field , and that u is countably additive and bounded .**Suppose**that every continuous function is u - measurable . Show that { * contains every Borel set . 24**Suppose**that S is a ...Page 225

Let U be a bounded open set in the complex plane , and let B denote the boundary of U. We

Let U be a bounded open set in the complex plane , and let B denote the boundary of U. We

**suppose**that B consists of a finite collection of disjoint closed rectifiable Jordan curves ; that is , we**suppose**that B can be decomposed into ...Page 360

1-32 22

1-32 22

**Suppose**that ( Sn ) ( x ) = f ( x ) uniformly for every f in AC . Show that there exists a finite constant K such that for f in CBI , | ( S - 1 ) ( x ) SK ( v ( f , 0 , 27 ] ) + sup \ | ( x ) ) , O SX 2.7 .### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric neighborhood norm operator positive measure problem Proc Proof properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero