## Linear Operators: General theory |

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Page 20

Thus A , + X , and A is open , and

Thus A , + X , and A is open , and

**contains**a sphere S , = S ( P1 , & , ) with 0 ... By assumption , the set A , does not**contain**the open set S ( P1 ...Page 56

of the image of any neighborhood G of the element 0 in X

of the image of any neighborhood G of the element 0 in X

**contains**a neighborhood of the element 0 in Y. Since a - b is a continuous function of a and b ...Page 309

The set A S - U - 1 E , then

The set A S - U - 1 E , then

**contains**no atoms having measure greater than ε . It will now be shown that every measurable subset B of A**contains**a set F ...### 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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### Common terms and phrases

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