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Page 143
Expressions such as u - simple function , totally u - measurable function , u - measurable function , u - integrable function , etc. , do not change meaning when u is regarded as defined on E * . This is because these expressions refer ...
Expressions such as u - simple function , totally u - measurable function , u - measurable function , u - integrable function , etc. , do not change meaning when u is regarded as defined on E * . This is because these expressions refer ...
Page 326
Let 8x and nk have the same meaning as in the previous paragraph . Since each fx 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 ...
Let 8x and nk have the same meaning as in the previous paragraph . Since each fx 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 ...
Page 685
In order to be able to assign a meaning to the averages 1 a ( ii ) A ( Q ) = ( * t T ( t ) dt , 0 SO , O. ó which are to be our basic concern in this section , it will be desirable to supplement the algebraic condition ( i ) by a ...
In order to be able to assign a meaning to the averages 1 a ( ii ) A ( Q ) = ( * t T ( t ) dt , 0 SO , O. ó which are to be our basic concern in this section , it will be desirable to supplement the algebraic condition ( i ) by a ...
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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