## 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

If we put E ( E ) = { F € E F C E } it is clear that E ( E ) is a

If we put E ( E ) = { F € E F C E } it is clear that E ( E ) is a

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

The symbol will be used for the o -

The symbol will be used for the o -

**field**of sets in S determined by Ey . The family of all sets in S of the form S , XER with Ε ε Σ will be denoted by Σπ . 18 LEMMA . For each a the family In is a**field**of sets in S and Σ . = U ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

91 other sections not shown

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### Common terms and phrases

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