## Linear Operators, Part 1 |

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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

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

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