## 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**( E ) = In contrast to the terms real function , complex function ...Page 96

A

A

**set function**u defined on a family t of sets is said to be additive or finitely additive if u ( d ) = 0 and u ( A , U AZ .Page 184

We shall denote by E the family of all sets in the Cartesian product S = S , X .. ... Then there is a unique additive

We shall denote by E the family of all sets in the Cartesian product S = S , X .. ... Then there is a unique additive

**set function**u defined on the smallest ...### 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