## Linear Operators: General theory |

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Page 136

There is a uniquely determined smallest

There is a uniquely determined smallest

**field**and a uniquely determined smallest o -**field**containing a given family of sets . PROOF . There is at least one**field**, namely the**field**of all subsets of S , which contains a given family t ...Page 166

Suppose that E is a set in E. If we put E ( E ) = { F € E F C E } it Σ Σ ( ) FeEF is clear that E ( E ) is a

Suppose that E is a set in E. If we put E ( E ) = { F € E F C E } it Σ Σ ( ) FeEF is clear that E ( E ) is a

**field**of subsets of E , and that E ( E ) is the family of all sets AE , A € E , and that if & is a o -**field**, then E ( E ) is ...Page 201

There should be no confusion between the symbols Ez and Eą , for if a reduces to the single element a then the

There should be no confusion between the symbols Ez and Eą , for if a reduces to the single element a then the

**field**Ez is the o -**field**Eq . An elementary set in S is one of the form Paca Ex where E ...### 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