## Linear Operators, Part 1 |

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Page 112

A function f on S to X is

addition the equation limss \ fm ( s ) –In ( s ) [ 0 ( 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 { / n } of**u**-**integrable**simple functions converging to | in u - measure on S and satisfying inaddition the equation limss \ fm ( s ) –In ( s ) [ 0 ( 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 { \ /

n ...

A function f on S is

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

n ...

Page 180

The

Theorem 4 ) that 1 ) g ( ) is pe - integrable . Theorem 4 applies in the same

manner 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 1 ) g ( ) is pe - integrable . Theorem 4 applies in the same

manner to 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 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

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