## Linear Operators: General theory |

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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

... II.4.4 ( 70 ) Biorthogonal system , in a B - space , II.4.11 ( 71 ) Boolean algebra .

( See also Boolean ring ) definition , ( 43 ) properties , ( 44 ) representation of , (

44 ) Boolean ring , definition , ( 40 ) representation of , 1.12.1 ( 41 )

... II.4.4 ( 70 ) Biorthogonal system , in a B - space , II.4.11 ( 71 ) Boolean algebra .

( See also Boolean ring ) definition , ( 43 ) properties , ( 44 ) representation of , (

44 ) Boolean ring , definition , ( 40 ) representation of , 1.12.1 ( 41 )

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

### Common terms and phrases

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 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