## Linear Operators: General theory |

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

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

**regular**if for each Ee & and > 0 there is a set F in whose closure is contained in E and a set G in whose interior contains E such that ...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 , E , u , X ) .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 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric neighborhood norm obtained operator positive measure problem Proc PROOF properties proved regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero