## Linear Operators: General theory |

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Page 262

Since the integral [ st ( s ) u ( ds ) satisfies the inequality sup \ | ( s ) [ v ( u , S ) , it is

theorem is a converse to this statement . 2 THEOREM . If S is normal , there is an

...

Since the integral [ st ( s ) u ( ds ) satisfies the inequality sup \ | ( s ) [ v ( u , S ) , it is

**clear**that the integral is a continuous linear functional on C ( S ) . The followingtheorem is a converse to this statement . 2 THEOREM . If S is normal , there is an

...

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 ) C T ( d ) if ε < 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

It is

if F4 € £g , then S - F , € £g , and that if F1 , F2 € £z with F F , = 0 , then Fi UF , € £

g . It follows that Ez is a field . If { Fx } is a sequence of disjoint elements of Eg ...

It is

**clear**that if F , and F , are elements of £3 , then F , F , € £g . It is also**clear**thatif F4 € £g , then S - F , € £g , and that if F1 , F2 € £z with F F , = 0 , then Fi UF , € £

g . It follows that Ez is a field . If { Fx } is a sequence of disjoint elements of Eg ...

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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