## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 76

Page 100

Any statement concerning the points of S is said to hold u - almost

or , if u is understood , simply almost

true except for those points s in a u - null set . The phrase " almost

Any statement concerning the points of S is said to hold u - almost

**everywhere**,or , if u is understood , simply almost

**everywhere**, or for almost all s in S , if it istrue except for those points s in a u - null set . The phrase " almost

**everywhere**...Page 151

( Lebesgue dominated convergence theorem ) Let 1 sp < oo , let ( S , E , u ) be a

measure space , and let { fn } be a sequence of functions in L ( S , E , „ , X )

converging almost

function g in ...

( Lebesgue dominated convergence theorem ) Let 1 sp < oo , let ( S , E , u ) be a

measure space , and let { fn } be a sequence of functions in L ( S , E , „ , X )

converging almost

**everywhere**to a function f . Suppose that there exists afunction g in ...

Page 676

For such a vector h we have A ( T , n ) h = f + ( I – T " ) g / n , and thus , for almost

all s in S , we have | AT , n ) ( h , s ) - | ( s ) = 2glon → 0 . This shows that AT , nbh

converges almost

For such a vector h we have A ( T , n ) h = f + ( I – T " ) g / n , and thus , for almost

all s in S , we have | AT , n ) ( h , s ) - | ( s ) = 2glon → 0 . This shows that AT , nbh

converges almost

**everywhere**for every h in a dense set in L , and , by Lemma 5 ...### What people are saying - Write a review

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

### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

### Common terms and phrases

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