## Linear Operators: General theory |

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Page 95

Finitely Additive

Finitely Additive

**Set Functions**In contrast to the terms real function , complex function , etc. , where the adjectives real and complex refer to the range of the function , the term**set function**is commonly used in mathematics for a ...Page 96

A

A

**set function**u defined on a family t of sets is said to be additive or finitely additive if uld ) = 0 and u ( A ... For an example of a finitely additive**set function**, let S = ( 0 , 1 ) 0 ) and let 7 be the family of intervals I ...Page 131

Let i , u be finitely additive

Let i , u be finitely additive

**set functions**defined on a field E. Then 2 is said to be continuous with respect to u or simply - continuous , if lim 2 ( E ) = 0 . v ( u , E ) - > 0 The function 2 is said to be u - singular if there is 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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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