## Linear Operators: General theory |

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Page 169

3 Suppose that S is the interval ( - 00 , + 00 ) , that is the field of finite sums of

intervals half open on the left , and that u is the restriction of Lebesgue measure

to E ...

**Show**that there need not exist any set E € £ containing A such that v ( u , E ) = 0 .3 Suppose that S is the interval ( - 00 , + 00 ) , that is the field of finite sums of

intervals half open on the left , and that u is the restriction of Lebesgue measure

to E ...

Page 358

projection Sn in each of the spaces Lp , BV , CBV , AC , C1k ) , 1 sp oo , k = 0 , 1 ,

2 , . . . , 00 .

**Show**that Snt is given by the formula ( Sf ) ( x ) = $ . * E , ( x , y ) f ( y ) dy , and is aprojection Sn in each of the spaces Lp , BV , CBV , AC , C1k ) , 1 sp oo , k = 0 , 1 ,

2 , . . . , 00 .

**Show**that the range of Sn lies in C ) . 3**Show**that Sn I strongly in ...Page 360

21

. n . system is localized if and only if max En ( x , y ) SM , < oo for each ε > 0 . l -

ulze 22 Suppose that ( Sn ) ( x ) + f ( x ) uniformly for every f in AC .

there ...

21

**Show**that if sé En ( x , z ) dz SM , then the convergence of Snj for a given c . o. n . system is localized if and only if max En ( x , y ) SM , < oo for each ε > 0 . l -

ulze 22 Suppose that ( Sn ) ( x ) + f ( x ) uniformly for every f in AC .

**Show**thatthere ...

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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