## Linear Operators: General theory |

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Page 28

1 : D → X be a generalized sequence of elements in a metric space X . We call f a

generalized Cauchy sequence in X , if , for each ε > 0 , there

such that elf ( p ) , f ( q ) ) < ε if p 2 do , q do . 5 LEMMA . If f is a generalized

Cauchy ...

1 : D → X be a generalized sequence of elements in a metric space X . We call f a

generalized Cauchy sequence in X , if , for each ε > 0 , there

**exists**a do € D ,such that elf ( p ) , f ( q ) ) < ε if p 2 do , q do . 5 LEMMA . If f is a generalized

Cauchy ...

Page 353

Let M , be the space of all bounded 2 - measurable functions f defined on R such

that lim f ( x )

85 Let K ( x , y ) be a 2 x à measurable function on RX R . Suppose that K ( x , y )

...

Let M , be the space of all bounded 2 - measurable functions f defined on R such

that lim f ( x )

**exists**. Putting H = lub \ ( x ) ] , OS & < show that M , is a B - space .85 Let K ( x , y ) be a 2 x à measurable function on RX R . Suppose that K ( x , y )

...

Page 362

Under the hypotheses of Exercise 37 , show that there

( x ) øn ( x ) dx if and only if the functions o n humnandin ( x ) , m 2 1 , are

uniformly bounded and equicontinuous . 39 Let { an } , - 00 < n < too , be a

bounded ...

Under the hypotheses of Exercise 37 , show that there

**exists**f in C with an = Sa +( x ) øn ( x ) dx if and only if the functions o n humnandin ( x ) , m 2 1 , are

uniformly bounded and equicontinuous . 39 Let { an } , - 00 < n < too , be a

bounded ...

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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