## Linear Operators: General theory |

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Page 68

The space X is said to be weakly complete if every weak Cauchy sequence has a

weak

such a way that they become Hausdorff spaces in which the notion of

convergence ...

The space X is said to be weakly complete if every weak Cauchy sequence has a

weak

**limit**. In Chapter V , a topology is introduced in certain linear spaces insuch a way that they become Hausdorff spaces in which the notion of

convergence ...

Page 126

A measure is a complex or extended real valued countably additive set function

whose domain is a o - field . Throughout this section ( S , E , u ) is assumed to be

a measure space . Suppose that { En } is a sequence of sets . We define the

...

A measure is a complex or extended real valued countably additive set function

whose domain is a o - field . Throughout this section ( S , E , u ) is assumed to be

a measure space . Suppose that { En } is a sequence of sets . We define the

**limit**...

Page 127

It is evident that such a sequence has the

sequence { En } is one for which En . En + , n = 1 , 2 , . . . . Such a sequence has

the

non ...

It is evident that such a sequence has the

**limit**Un En . A non - increasingsequence { En } is one for which En . En + , n = 1 , 2 , . . . . Such a sequence has

the

**limit**n - En . A monotone sequence is one which is either non - decreasing ornon ...

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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