## Linear Operators: General theory |

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Page 132

Then E , C EU EE € N which contradicts the maximality of Eg , and proves that a is u - continuous . Q.E.D. = 5.

Then E , C EU EE € N which contradicts the maximality of Eg , and proves that a is u - continuous . Q.E.D. = 5.

**Extensions**of Set Functions A given ...Page 136

( Hahn

( Hahn

**extension**) Every countably additive non - negative extended real valued set function u on a field has a countably additive non - negative**extension**...Page 143

Then the function u with domain { * is known as the Lebesgue

Then the function u with domain { * is known as the Lebesgue

**extension**of u . The o - field * is known as the Lebesgue**extension**( relative to u ) of the o ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

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