## Linear Operators: General theory |

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CHAPTER III Integration and

CHAPTER III Integration and

**Set Functions**1. Finitely Additive**Set Functions**In contrast to the terms real function , complex function , etc. , where the ...Page 96

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**set function**u defined on a family t of sets is said to be additive or finitely additive if uld ) = 0 and M ( A , U AZ .Page 837

A on Abel summability , of series , II.4.42 ( 76 ) Abelian group , ( 34 ) Absolutely continuous functions , definition , IV.2.22 ( 242 )

A on Abel summability , of series , II.4.42 ( 76 ) Abelian group , ( 34 ) Absolutely continuous functions , definition , IV.2.22 ( 242 )

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

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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