## Linear Operators: General theory |

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Page 143

... u - integrable function , etc. , do not change

defined on 2 * . This is because these expressions refer to equivalence classes of

functions differing by a u - null function rather than the functions themselves .

... u - integrable function , etc. , do not change

**meaning**when u is regarded asdefined on 2 * . This is because these expressions refer to equivalence classes of

functions differing by a u - null function rather than the functions themselves .

Page 326

Let 8x and nx have the same

fk is u - integrable it follows from Egoroff's theorem ( III.6.12 ) and the second

paragraph of the proof of Theorem III.2.22 that there is a simple function gk and a

set ...

Let 8x and nx have the same

**meaning**as in the previous paragraph . Since eachfk is u - integrable it follows from Egoroff's theorem ( III.6.12 ) and the second

paragraph of the proof of Theorem III.2.22 that there is a simple function gk and a

set ...

Page 685

In order to be able to assign a

a , which are to be our basic concern in this section , it will be desirable to

supplement the algebraic condition ( i ) by a condition concerning the analytical ...

In order to be able to assign a

**meaning**to the averages 1 ( ii ) A ( Q ) T ( t ) dt , 0 <a , which are to be our basic concern in this section , it will be desirable to

supplement the algebraic condition ( i ) by a condition concerning the analytical ...

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric neighborhood norm operator positive measure problem Proc PROOF properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero