## Linear Operators: General theory |

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Page 137

An additive set function и M defined on a field of subsets of a topological space S is said to be

An additive set function и M defined on a field of subsets of a topological space S is said to be

**regular**if for each Ee and ε > 0 there is a set F in whose closure is contained in E and a set G in whose interior contains E such that su ...Page 170

17 Suppose that S is a normal topological space and that u is

17 Suppose that S is a normal topological space and that u is

**regular**and defined on the field of Borel sets in S. Show that if X is separable , the set of continuous functions in TM ( S , E , u , X ) is dense in TM ( S , & ...Page 853

( See Reflexivity )

( See Reflexivity )

**Regular**closure , ( 462–463 )**Regular**convexity , ( 462–463 )**Regular**element in a ring , ( 40 )**Regular**method of summability , II.4.35 ( 75 )**Regular**set function . ( See also Set function ) additional properties ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

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Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero