## 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 634

Since p ( E ) is open if E is open , it follows immediately that p ( E ) is a

Since p ( E ) is open if E is open , it follows immediately that p ( E ) is a

**Borel**set if E is a**Borel**set . Now let E be a**Borel**set of measure zero . By Fubini's theorem ( III.11.9 ) , we have S **** Xp ( E ) ( s , t ) ds dt = ZE ...Page 838

... ( 40 ) representation of , 1.12.1 ( 41 )

... ( 40 ) representation of , 1.12.1 ( 41 )

**Borel**field of sets , definition , II1.5.10 - ( 137 )**Borel**( or**Borel**... 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

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

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Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero