## Linear Operators: General theory |

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Page 95

Finitely Additive Set

process is

integral v ...

Finitely Additive Set

**Functions**In contrast to the terms real**function**, complex**function**, etc . , where the adjectives real and ... Thus , even if the integrationprocess is

**defined**with respect to a scalar valued set**function**u , the resultingintegral v ...

Page 98

The total variation of an additive set

S is also additive on E . PROOF . Let { A ; } be a finite sequence of disjoint sets in

with ACEUF where E , F € £ and EF = $ . Let E ; = EAi , Fi = FA , then Elu ( A ...

The total variation of an additive set

**function defined**on a field of subsets of a setS is also additive on E . PROOF . Let { A ; } be a finite sequence of disjoint sets in

with ACEUF where E , F € £ and EF = $ . Let E ; = EAi , Fi = FA , then Elu ( A ...

Page 101

SES If for some null set N the restriction off to S - N has its values in a separable

set , the

as essentially compact valued are

SES If for some null set N the restriction off to S - N has its values in a separable

set , the

**function**f is said to be i - essentially separably valued . Expressions suchas essentially compact valued are

**defined**similarly . In the example above ...### What people are saying - Write a review

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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