## Linear Operators: General theory |

### From inside the book

Results 1-3 of 70

Page 143

The measure of Lebesgue in an interval [ a , b ] of real numbers may be defined

as the Lebesgue extension of the

measurable sets in [ a , b ] are the sets in the Lebesgue extension ( relative to

The measure of Lebesgue in an interval [ a , b ] of real numbers may be defined

as the Lebesgue extension of the

**Borel**measure in [ a , b ] . The Lebesguemeasurable sets in [ a , b ] are the sets in the Lebesgue extension ( relative to

**Borel**...Page 838

10 ( 137 )

) III . 13 . 8 ( 223 )

5 ( 60 ) in a partially ordered set , I . 2 . 3 ( 4 ) in the ( extended ) real number ...

10 ( 137 )

**Borel**measure ( or**Borel**- Lebesgue measure ) , construction of , ( 139) III . 13 . 8 ( 223 )

**Borel**- Stieltjes measure , ( 142 ) Bound , of an operator , II . 3 .5 ( 60 ) in a partially ordered set , I . 2 . 3 ( 4 ) in the ( extended ) real number ...

Page 838

10 ( 137 )

) III . 13 . 8 ( 223 )

5 ( 60 ) in a partially ordered set , I . 2 . 3 ( 4 ) in the extended ) real number ...

10 ( 137 )

**Borel**measure ( or**Borel**- Lebesgue measure ) , construction of , ( 139) III . 13 . 8 ( 223 )

**Borel**- Stieltjes measure , ( 142 ) Bound , of an operator , II . 3 .5 ( 60 ) in a partially ordered set , I . 2 . 3 ( 4 ) in the extended ) real number ...

### What people are saying - Write a review

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

### Contents

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Three Basic Principles of Linear Analysis | 49 |

Copyright | |

50 other sections not shown

### Other editions - View all

### Common terms and phrases

analytic applied arbitrary assumed B-space Borel bounded called Chapter clear closed complex condition Consequently constant contains continuous functions continuous linear converges Corollary countably additive defined DEFINITION denote dense determined dimensional disjoint element equation equivalent everywhere Exercise exists extended field finite follows formula function defined function f given Hence Hilbert identity implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear map linear operator linear space meaning metric space neighborhood norm obtained operator positive measure space projection PROOF properties proved range reflexive regular respect satisfies scalar seen separable sequence sequentially set function Show shown statement strongly subset subspace sufficient Suppose Theorem theory tion topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero