## Linear Operators: General theory |

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Page 262

Since the integral [ st ( s ) u ( ds ) satisfies the inequality 1st ( s ) p ( ds ) = sup \ t ( s ) 0 ( 11 , S ) , 8 it is

Since the integral [ st ( s ) u ( ds ) satisfies the inequality 1st ( s ) p ( ds ) = sup \ t ( s ) 0 ( 11 , S ) , 8 it is

**clear**that the integral is a continuous linear functional on C ( S ) . The following theorem is a converse to this ...Page 282

It is

It is

**clear**that T ( 8 ) CT ( d ) if € < d and that -te T ( E ) whenever te T ( € ) . The function f is said to be almost periodic if it is continuous and if for every e > 0 there is an L L ( 8 ) > 0 such that every interval in R of ...Page 292

Since it is 9

Since it is 9

**clear**that Σ32 ΣΙ , we conclude that Σ3 2Σ , from which the desired result follows . Q.E.D. THEOREM . A subset K of L ( S , E , u ) is weakly sequentially compact if and only if it is bounded and the countable additivity ...### 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 | |

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