## Linear Operators: General theory |

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Page 24

Since { an } is a Cauchy sequence , and f is uniformly

Since { an } is a Cauchy sequence , and f is uniformly

**continuous**, the sequence { f ( an ) } is also a Cauchy sequence . Since Y is complete , there is a ...Page 131

Let i , u be finitely additive set functions defined on a field E. Then 2 is said to be

Let i , u be finitely additive set functions defined on a field E. Then 2 is said to be

**continuous**with respect to u or simply u -**continuous**, if lim 2 ( E ) ...Page 454

Now , N ( p ) is a

Now , N ( p ) is a

**continuous**function of p . For , if pm + p , and N ( Pn ) -1+ N ( p ) , then since K is compact , { N ( px ) } has a convergent ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

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### Common terms and phrases

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