## Linear Operators: General theory |

### From inside the book

Results 1-3 of 87

Page 95

Finitely Additive Set

Finitely Additive Set

**Functions**In contrast to the terms real**function**, complex**function**, etc. , where the adjectives ... Thus , even if the integration process is**defined**with respect to a scalar valued set**function**u , the resulting ...Page 98

The total variation of an additive set

The total variation of an additive set

**function defined**on a field E of subsets of a set S is also additive on 2 . PROOF . Let { A ; } be a finite sequence of disjoint sets in with ACEUF where E , F and EF = $ .Page 101

SES SES If for some null set N the restriction of f to S - N has its values in a separable set , the

SES SES If for some null set N the restriction of f to S - N has its values in a separable set , the

**function**f is said to be įl - essentially separably valued . Expressions such as essentially compact valued are**defined**similarly .### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

91 other sections not shown

### Other editions - View all

### 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