## Linear Operators: General theory |

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Results 1-3 of 86

Page 188

It is clear that the measure has the property n = 1 u ( PE ) = IT ui ( E ; ) , E , s and it

follows from the uniqueness part of ... Q.E.D. As in the case of finite

from ...

It is clear that the measure has the property n = 1 u ( PE ) = IT ui ( E ; ) , E , s and it

follows from the uniqueness part of ... Q.E.D. As in the case of finite

**measure****spaces**we shall call the**measure space**( S , E , u ) constructed in Corollary 6from ...

Page 838

7 ( 266 ) remarks concerning , ( 382 ) Atom , in a

Automorphisms , in groups , ( 35 ) B - space ( or Banach space ) , basic

properties of , Chap . II definition , II . 3 . 2 ( 59 ) integration , Chap . III special B -

spaces ...

7 ( 266 ) remarks concerning , ( 382 ) Atom , in a

**measure space**, IV . 9 . 6 ( 308 )Automorphisms , in groups , ( 35 ) B - space ( or Banach space ) , basic

properties of , Chap . II definition , II . 3 . 2 ( 59 ) integration , Chap . III special B -

spaces ...

Page 849

as a study of TM , IV.11 , IV.15 a topological linear

171 )

Borel or Borel - Lebesgue , ( 139 ) Borel - Stieltjes , ( 142 ) decomposition of .

as a study of TM , IV.11 , IV.15 a topological linear

**space**, III.9.7 ( 169 ) , III.9.28 (171 )

**Measurable**set , definition , III.4.3 ( 126 )**Measure**. ( See also Set function )Borel or Borel - Lebesgue , ( 139 ) Borel - Stieltjes , ( 142 ) decomposition of .

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### Contents

Preliminary Concepts 1 1 Preliminary Concepts | 1 |

B Topological Preliminaries 10 B Topological Preliminaries | 10 |

Metric Spaces | 18 |

Copyright | |

80 other sections not shown

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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