## Linear Operators, Part 1 |

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Page 52

This fact is established in

space will be needed . It is defined just as it is in a linear topological space ( cf.

Definition 7 ) . The following

...

This fact is established in

**Theorem**12. The notion of a bounded set in an F -space will be needed . It is defined just as it is in a linear topological space ( cf.

Definition 7 ) . The following

**theorem**, a principle of equi - continuity , is the basic...

Page 219

Instead of proving

the much more general question of when lim ( K , ( s , t ) / ( s ) ds = f ( t ) in the

Lebesgue set of f , where the kernels K , ( s , t ) are not necessarily positive or

even ...

Instead of proving

**Theorem**10 directly we shall consider in**Theorem**11 belowthe much more general question of when lim ( K , ( s , t ) / ( s ) ds = f ( t ) in the

Lebesgue set of f , where the kernels K , ( s , t ) are not necessarily positive or

even ...

Page 383

Conditions that are necessary as well as sufficient were not to come for a number

of years . The notion of the quasi - uniform convergence of a sequence of

functions was introduced in 1884 by Arzelą [ 1 ] to whom

the ...

Conditions that are necessary as well as sufficient were not to come for a number

of years . The notion of the quasi - uniform convergence of a sequence of

functions was introduced in 1884 by Arzelą [ 1 ] to whom

**Theorem**6.11 is due inthe ...

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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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Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero