## Linear Operators, Part 1 |

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Page 112

A function f on S to 3 is

simple functions converging to f in u-measure on S and satisfying in addition the

equation lims, i.(s)—i.(s)p(u, ds) = 0. Such a sequence of

A function f on S to 3 is

**u**-**integrable**on S if there is a sequence {fi} of**u**-**integrable**simple functions converging to f in u-measure on S and satisfying in addition the

equation lims, i.(s)—i.(s)p(u, ds) = 0. Such a sequence of

**u**-**integrable**simple ...Page 113

A function f on S is

so is f(-). If {f,} is a sequence of p-integrable simple functions determining f in

accordance with the preceding definition, then the sequence {|f,(:)} determines |f

(-) ...

A function f on S is

**u**-**integrable**if and only if it is v(u)-integrable. If f is**u**-**integrable**so is f(-). If {f,} is a sequence of p-integrable simple functions determining f in

accordance with the preceding definition, then the sequence {|f,(:)} determines |f

(-) ...

Page 180

Suppose that g is A-integrable. By Lemma 3, fg is measurable. The

of fg follows from Theorem 2.22 when it is observed (by Theorem 4) that f(-)g(') is

Suppose that g is A-integrable. By Lemma 3, fg is measurable. The

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

**u**-**integrable**. Theorem 4 applies in the same manner to prove the 2-integrability ...### What people are saying - Write a review

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### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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