## Linear Operators: General theory |

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23

additive and bounded.

Show that Z* contains every Borel set. 24

topological ...

23

**Suppose**that S is a metric space, that Z is a <x-field, and that fi is countablyadditive and bounded.

**Suppose**that every continuous function is //-measurable.Show that Z* contains every Borel set. 24

**Suppose**that S is a compacttopological ...

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 B ...

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 B ...

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a finite constant K such that for / in CBV, \(S„f)(x)\ <K(v(f, [0, 2jt]) + sup 0 ^ x ^ 2n.

28

22

**Suppose**that (S^)(x) -*□ f(x) uniformly for every / in AC. Show that there existsa finite constant K such that for / in CBV, \(S„f)(x)\ <K(v(f, [0, 2jt]) + sup 0 ^ x ^ 2n.

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**Suppose**that (') (Snf)(x) -+f(x) uniformly in x for / in AC. (ii) The convergence ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

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