## Linear Operators: General theory |

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Page 95

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

INTEGRATION AND

INTEGRATION AND

**SET FUNCTIONS**III.1.2 2 DEFINITION . A**set function**u defined on a family t of sets is said to be additive or finitely additive it ud O and ...Page 184

For i = 1 , ... , n , let u ; be a finitely additive complex valued

For i = 1 , ... , n , let u ; be a finitely additive complex valued

**set function**defined on a field of subsets of a set S. Then there is a unique additive ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain 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 mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero