## Linear Operators: General theory |

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Page 140

An

An

**interval**is a set of points in the extended real number system which has one of the forms : [ a , b ] { sla S8 = b } ... The number a is called the left end point and b the right end point of any of these**intervals**.Page 141

–t ) 0 i = n + 1 The argument may be repeated by defining Ez = an , -c . and choosing appropriate points in the

–t ) 0 i = n + 1 The argument may be repeated by defining Ez = an , -c . and choosing appropriate points in the

**interval**( c , c + ez ] . By induction , it is clear that for every integer k = 1 , 2 , ... , there are points az , bi with ...Page 223

5 Let h be a function of bounded variation on the

5 Let h be a function of bounded variation on the

**interval**( a , b ) and continuous on the right . Let g be a function defined on ( a , b ) such that the Lebesgue - Stieltjes integral I = Såg ( s ) dh ( s ) exists .### 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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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