## Linear Operators: General theory |

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Page 107

Now let g be a continuous

Now let g be a continuous

**function**defined on the field of scalars 8 and let B ... Given € > 0 there is , as before , a constant M and a**set**A , such that r ...Page 136

Q.E.D. The smallest field containing a family of

Q.E.D. The smallest field containing a family of

**sets**will sometimes be called ... Let Ebe a field of subsets of a**set**S , and extended real valued**function**...Page 203

Then there is a unique countably additive

Then there is a unique countably additive

**set function**u defined on the o - field determined by the elementary sets in S with the ...### 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