## Linear Operators: General theory |

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Page 132

Nelson Dunford, Jacob T. Schwartz. This lemma shows that if each member of a

generalized sequence { 2x } of finite ,

continuous and if lim , 2 , ( E ) = 2 ( E ) , E££ , where a is also a finite ,

Nelson Dunford, Jacob T. Schwartz. 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**...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 233

All of these integrals are

present a Lebesgue type theory of integration of a scalar function with respect to

a

...

All of these integrals are

**countably additive**integrals . In Section IV . 10 we willpresent a Lebesgue type theory of integration of a scalar function with respect to

a

**countably additive**vector valued measure . Instances in which both the function...

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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