## Linear Operators: General theory |

### From inside the book

Results 1-3 of 63

Page 136

an 6 LEMMA . There is a uniquely

at least one field , namely the field of all subsets of S , which contains a given

family t .

an 6 LEMMA . There is a uniquely

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

family t .

Page 143

Similarly , the Lebesgue - Stieltjes measure

bounded variation on a finite or infinite interval is the Lebesgue extension of the

Borel - Stieltjes measure

Similarly , the Lebesgue - Stieltjes measure

**determined**by a function f ofbounded variation on a finite or infinite interval is the Lebesgue extension of the

Borel - Stieltjes measure

**determined**by f . If u is either the Borel - Stieltjes or the ...Page 455

Let G Un = 1 Yn ; then f is

subset of X * , there exists a denumerable subset G , of X * such that each fe F is

...

Let G Un = 1 Yn ; then f is

**determined**by G. It follows that if F is a denumerablesubset of X * , there exists a denumerable subset G , of X * such that each fe F is

**determined**by G. We can even assert that each continuous linear functional f can...

### What people are saying - Write a review

User Review - Flag as inappropriate

i want to read

### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

### Other editions - View all

### Common terms and phrases

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