## Linear Operators: General theory |

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CHAPTER III Integration and Set

contrast to the terms real

real and complex refer to the range of the

CHAPTER III Integration and Set

**Functions**1 . Finitely Additive Set**Functions**Incontrast to the terms real

**function**, complex**function**, etc . , where the adjectivesreal and complex refer to the range of the

**function**, the term set**function**is ...Page 103

space of all

rarely the case and so a slight detour will be made . 3 DEFINITION . The

on S to X is said to be a u - null

space of all

**functions**which map S into X ( see 1 . 6 . 1 ) . Unfortunately , this israrely the case and so a slight detour will be made . 3 DEFINITION . The

**function**fon S to X is said to be a u - null

**function**or , when u is understood , simply a null ...Page 165

Since a ll - simple

measurable

is evident that f is also a u - integrable simple

Since a ll - simple

**function**is clearly u - simple , it follows immediately that a My -measurable

**function**is u - measurable . If f is a My - integrable simple**function**, itis evident that f is also a u - integrable simple

**function**, and that set ( s ) py ( ds ) ...### What people are saying - Write a review

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad domain elements 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 operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen semi-group 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