## Linear Operators: General theory |

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Page 112

A function f on S to X is

addition the equation lim s \ / m ( s ) - In ( 8 ) | v ( u , ds ) = 0 . Such a sequence of

u ...

A function f on S to X is

**u**-**integrable**on S if there is a sequence { In } of**u**-**integrable**simple functions converging to f in u - measure on S and satisfying inaddition the equation lim s \ / m ( s ) - In ( 8 ) | v ( u , ds ) = 0 . Such a sequence of

u ...

Page 113

A function f on S is

determining f in accordance with the preceding definition , then the sequence { \

In ( o ) ...

A function f on S is

**u**-**integrable**if and only if it is v ( ul ) -integrable . If f is**u**-**integrable**so is \ | ( • ) . 1 } { In } is a sequence of**u**-**integrable**simple functionsdetermining f in accordance with the preceding definition , then the sequence { \

In ( o ) ...

Page 180

The

Theorem 4 ) that f ( g ( ) is

to prove the 2 - integrability of g when it is assumed that fg is

The

**u**-**integrability**of fg follows from Theorem 2.22 when it is observed ( byTheorem 4 ) that f ( g ( ) is

**u**-**integrable**. Theorem 4 applies in the same mannerto prove the 2 - integrability of g when it is assumed that fg is

**u**-**integrable**.### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

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