## Linear Operators, Part 1 |

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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

S ) . The following theorem is a converse to this statement . 2 THEOREM .

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 statement . 2 THEOREM .

Page 282

It is

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 length L contains at least one ...

It is

**clear**that T ( 8 ) CT ( d ) if € < d and that -te T ( E ) whenever te T ( € ) . Thefunction 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 length L contains at least one ...

Page 292

Let E , be the family of all sets E in E for which lim un ( EF ) exists for each Fe E1 ,

and let E , be the family of all sets E in E , for which EF e E , for each Fe En . It is

...

Let E , be the family of all sets E in E for which lim un ( EF ) exists for each Fe E1 ,

and let E , be the family of all sets E in E , for which EF e E , for each Fe En . It is

**clear**that if F , and F , are elements of E3 , then F F2 € Eg . It is also**clear**that if F...

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

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