## 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

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 Lebesgue measurable sets in [ a , b ] are the sets in the Lebesgue extension ( relative to ...Page 643

It was shown at the beginning of the proof of Lemma 1.25 that if E is a

It was shown at the beginning of the proof of Lemma 1.25 that if E is a

**Borel**subset of the real line , the set P ( E ) = { ( x , y ) \ v + y e E } is a**Borel**subset of the plane . For each**Borel**subset E of the real line let Y ( E ) ...Page 838

... 1.12.1 ( 41 )

... 1.12.1 ( 41 )

**Borel**field of sets , definition , III.5.10 ( 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 ) ...### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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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