## 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 | FC E } it is clear that ( E ) is a

Suppose that E is a set in E. If we put E ( E ) = { F € E | FC E } it is clear that ( 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 family of elementary sets in S will be denoted by E and the

The family of elementary sets in S will be denoted by E and the

**field**of sets in S determined by E will be denoted by £ ,. The symbol will be used for the o -**field**of sets in S determined by ,. The family of all sets in S of the form S ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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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 Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric neighborhood norm obtained operator positive measure problem Proc PROOF properties proved regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero