## Linear Operators: General theory |

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Page 95

Finitely Additive Set Functions In contrast to the terms real function , complex ... A set function is a

Finitely Additive Set Functions In contrast to the terms real function , complex ... A set function is a

**function defined**on a family of sets , and having ...Page 98

The total variation of an additive set

The total variation of an additive set

**function defined**on a field E of subsets of a set S is also additive on 2 . PROOF . Let { A ; } be a finite sequence ...Page 101

In these sections f will be a vector valued

In these sections f will be a vector valued

**function defined**on a set S and u a finitely additive set**function defined**on a field of subsets of S. It will ...### 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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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero