## Linear Operators: General theory |

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Page 147

... it

... it

**vanishes**almost everyrohere . li j is u - integrable then Set ( s ) u ( ds ) = 0 for every E in E if and only if 1**vanishes**almost everywhere . Proof . It is clear that a function**vanishing**almost everywhere is a null function .Page 334

... and hence it follows that \ W ( « ) – W ( y ) ] = [ W ( x − y ) ) , X , Y E € X. This proves that W is continuous at every point of X. By ( ii ) , W

... and hence it follows that \ W ( « ) – W ( y ) ] = [ W ( x − y ) ) , X , Y E € X. This proves that W is continuous at every point of X. By ( ii ) , W

**vanishes**on a set which is dense in X ; consequently W**vanishes**identically .Page 572

Suppose that does not

Suppose that does not

**vanish**identically in any neighborhood of 24. ... In the same way we see that either |**vanishes**identically in a neighborhood of his i 2 , .. ... , r , or 2 , is a pole of o ( T ) and f has a zero of order at least ...### 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 | |

87 other sections not shown

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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