## Linear Operators, Part 1 |

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Page 311

Proof . Consider the closed subspace B ( S , E ) of B ( S ) . According to Theorems

6.18 and 6.20 there is a compact Hausdorff space S , such that B ( S , E ) is

equivalent to C ( S . ) . Theorem 5.1 shows that there is an isometric

æ ...

Proof . Consider the closed subspace B ( S , E ) of B ( S ) . According to Theorems

6.18 and 6.20 there is a compact Hausdorff space S , such that B ( S , E ) is

equivalent to C ( S . ) . Theorem 5.1 shows that there is an isometric

**isomorphism**æ ...

Page 312

Let S , be a compact Hausdorff space such that B ( S , E ) is isometrically

EUF ) = t ( E ) ...

Let S , be a compact Hausdorff space such that B ( S , E ) is isometrically

**isomorphic**with C ( S ) . ... The correspondence Xe + % E , establishes an**isomorphism**7 of the field & onto the field of all open and closed sets in S , i.e. , t (EUF ) = t ( E ) ...

Page 313

The correspondence U : \ → \ ly is an isometric

( Sı . Ey ) . ( c ) If E , is in E , then v ( M , E ) = v ( U ( u ) , E ) for all in ba ( S , E ) .

PROOF . Recalling that t is an

...

The correspondence U : \ → \ ly is an isometric

**isomorphism**of ba ( S , E ) onto ca( Sı . Ey ) . ( c ) If E , is in E , then v ( M , E ) = v ( U ( u ) , E ) for all in ba ( S , E ) .

PROOF . Recalling that t is an

**isomorphism**of onto E , it is clear that the mapping...

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

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