## 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 E | F C E } it is clear that E ( E ) is a

Suppose that E is a set in E. If we put E ( E ) = { F e 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 € E , 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 7. The family of all sets in S of the form Sq , XER with E , ε Σ will be denoted by Σπ . Q € 18 LEMMA . For each r the family en is a**field**of sets in S and Σ , = Ο Σπ ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain 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 mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero