## Linear Operators: General theory |

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23

additive and bounded .

. Show that £ * contains every Borel set . 24

23

**Suppose**that S is a metric space , that is a o - field , and that u is countablyadditive and bounded .

**Suppose**that every continuous function is u - measurable. Show that £ * contains every Borel set . 24

**Suppose**that S is a compact ...Page 225

Let U be a bounded open set in the complex plane , and let B denote the

boundary of U . We

rectifiable Jordan curves ; that is , we

union ...

Let U be a bounded open set in the complex plane , and let B denote the

boundary of U . We

**suppose**that B consists of a finite collection of disjoint closedrectifiable Jordan curves ; that is , we

**suppose**that B can be decomposed into theunion ...

Page 360

21 Show that if sé En ( x , z ) dz SM , then the convergence of Snj for a given c . o

. n . system is localized if and only if max En ( x , y ) SM , < oo for each ε > 0 . l -

ulze 22

there ...

21 Show that if sé En ( x , z ) dz SM , then the convergence of Snj for a given c . o

. n . system is localized if and only if max En ( x , y ) SM , < oo for each ε > 0 . l -

ulze 22

**Suppose**that ( Sn ) ( x ) + f ( x ) uniformly for every f in AC . Show thatthere ...

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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