## 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

Moore ...

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.Moore ...

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

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

of S - UM = En is either an atom of infinite measure or a null set . Show that no ...

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

**equivalent**to l if and only if there exists a countablecollection of atoms of finite measure { En } in such that every measurable subset

of S - UM = En is either an atom of infinite measure or a null set . Show that no ...

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### Contents

Preliminary Concepts 1 1 Preliminary Concepts | 1 |

B Topological Preliminaries 10 B Topological Preliminaries | 10 |

Metric Spaces | 18 |

Copyright | |

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