## Linear Operators: General theory |

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Page 48

The first occurrence of a maximum principle

principle ( as in Theorem 2 . 6 ) is in Hausdorff ( 1 ; p . 140 ] . Zorn [ 1 ] gave a

theorem essentially

...

The first occurrence of a maximum principle

**equivalent**to the well - orderingprinciple ( as in Theorem 2 . 6 ) is in Hausdorff ( 1 ; p . 140 ] . Zorn [ 1 ] gave a

theorem essentially

**equivalent**to Theorem 2 . 7 . A similar theorem is due to R . L...

Page 91

admits an

invariant metric and is complete under each invariant metric . Thus every

complete linear metric space can be metrized to be an F - space . Further , a

normed linear ...

admits an

**equivalent**metric under which it is complete , then G admits aninvariant metric and is complete under each invariant metric . Thus every

complete linear metric space can be metrized to be an F - space . Further , a

normed linear ...

Page 347

( b ) Show that L ( S , E , u ) is

countable collection of atoms of finite measure { En } in such that every

measurable subset of S - UC _ En is either an atom of infinite measure or a null

set . 50 Show that ...

( b ) Show that L ( S , E , u ) is

**equivalent**to l , if and only if there exists acountable collection of atoms of finite measure { En } in such that every

measurable subset of S - UC _ En is either an atom of infinite measure or a null

set . 50 Show that ...

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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