## Linear Operators: General theory |

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Page 132

This lemma shows that if each member of a generalized sequence { 2x } of finite ,

where a is also a finite ,

This lemma shows that if each member of a generalized sequence { 2x } of finite ,

**countably additive**measures is u - continuous and if lim , 2 , ( E ) = 2 ( E ) , E££ ,where a is also a finite ,

**countably additive**measure , then à is also u ...Page 136

( Hahn extension ) Every

set function u on a field E has a

the o - field determined by E . If u is o - finite on Ethen this extension is unique .

( Hahn extension ) Every

**countably additive**non - negative extended real valuedset function u on a field E has a

**countably additive**non - negative extension tothe o - field determined by E . If u is o - finite on Ethen this extension is unique .

Page 405

The measure Moo is

zero ; the measure u is not

Mac and , it is easy to see that ly is the union of a countable family of u - null sets .

The measure Moo is

**countably additive**; the subset l , of s is of Moo - measurezero ; the measure u is not

**countably additive**. In fact , using the relation betweenMac and , it is easy to see that ly is the union of a countable family of u - null sets .

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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