## Linear Operators: General theory |

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The Vitali - Hahn - Saks Theorem and Spaces of Measures . . 8 . Relativization of

Set Functions . ... 237 2 . A List of Special Spaces . . . . 238 3 . Finite Dimensional

Spaces . . . . . 244 4 . Hilbert Space . ... Linear

The Vitali - Hahn - Saks Theorem and Spaces of Measures . . 8 . Relativization of

Set Functions . ... 237 2 . A List of Special Spaces . . . . 238 3 . Finite Dimensional

Spaces . . . . . 244 4 . Hilbert Space . ... Linear

**Topological Spaces**.Page 238

During the course of the investigation a number of interesting special properties

of the spaces to be considered and ... is a

either the real B - space of all real valued bounded continuous functions on S or ...

During the course of the investigation a number of interesting special properties

of the spaces to be considered and ... is a

**topological space**, C ( S ) can denoteeither the real B - space of all real valued bounded continuous functions on S or ...

Page 838

6 ( 308 ) Automorphisms , in groups , ( 35 ) B -

properties of , Chap . II definition , II . 3 . 2 ( 59 ) integration , Chap ... of C -

, V . 8 . 8 ( 442 ) remarks on , ( 396 - 397 , 466 ) Base for a

6 ( 308 ) Automorphisms , in groups , ( 35 ) B -

**space**( or Banach**space**) , basicproperties of , Chap . II definition , II . 3 . 2 ( 59 ) integration , Chap ... of C -

**spaces**, V . 8 . 8 ( 442 ) remarks on , ( 396 - 397 , 466 ) Base for a

**topology**, criterion for ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

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### Common terms and phrases

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 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