## Linear Operators: General theory |

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Page 95

Finitely Additive Set Functions ( E ) = In contrast to the terms real function ... A set function is a

Finitely Additive Set Functions ( E ) = In contrast to the terms real function ... 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 of subsets of a set S is also additive on E. PROOF . Let { A ; } be a finite sequence of ...Page 182

For an additive set

For an additive set

**function**u , on E , the equation 4 ( 0-1 ( E ) ) = 42 ( E )**defines**an additive set**function**My on Ex . Moreover ( a ) ...### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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### Common terms and phrases

Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric neighborhood norm operator positive measure problem Proc PROOF properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero