## 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 a > 0 there is a set F in whose ...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 ...Page 853

... ( 88 ) examples of reflexive spaces , IV.15 properties , II.3.23–24 ( 67 ) , II.3.2829 ( 68–69 ) remarks on , ( 463 ) , ( 473 )

... ( 88 ) examples of reflexive spaces , IV.15 properties , II.3.23–24 ( 67 ) , II.3.2829 ( 68–69 ) remarks on , ( 463 ) , ( 473 )

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

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Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain 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 mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen 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