## Linear Operators: General theory |

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Page 95

In some cases that will be encountered the values of u are not scalars , but

customarily where integration is used in this text u is a scalar

f a vector ( or scalar )

defined ...

In some cases that will be encountered the values of u are not scalars , but

customarily where integration is used in this text u is a scalar

**valued**function andf a vector ( or scalar )

**valued**function . Thus , even if the integration process isdefined ...

Page 224

It will be assumed that the reader is familiar with the elementary theory of

complex

applied here to obtain the extensions which will be used later . Throughout this

section ...

It will be assumed that the reader is familiar with the elementary theory of

complex

**valued**analytic functions of one complex variable and this theory will beapplied here to obtain the extensions which will be used later . Throughout this

section ...

Page 323

A scalar

sequence { In } of simple functions such that ( i ) in ( s ) converges to f ( s ) u -

almost everywhere ; ( ii ) the sequence { Seln ( s ) u ( ds ) } converges in the norm

of X ...

A scalar

**valued**measurable function f is said to be integrable if there exists asequence { In } of simple functions such that ( i ) in ( s ) converges to f ( s ) u -

almost everywhere ; ( ii ) the sequence { Seln ( s ) u ( ds ) } converges in the norm

of X ...

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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