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Page 6
It will next be shown that P is admissible . The condition ( i ) is vacuously satisfied by P. To prove that P has the property ( ii ) , let x € P. It will be shown that if z € A , and > < f ( x ) , then f ( x ) = f ( x ) .
It will next be shown that P is admissible . The condition ( i ) is vacuously satisfied by P. To prove that P has the property ( ii ) , let x € P. It will be shown that if z € A , and > < f ( x ) , then f ( x ) = f ( x ) .
Page 156
More direct relationships between set functions and certain B - spaces are explicitly discussed in the next chapter , where it is shown that the conjugate spaces of some familiar B - spaces may be represented in terms of set functions .
More direct relationships between set functions and certain B - spaces are explicitly discussed in the next chapter , where it is shown that the conjugate spaces of some familiar B - spaces may be represented in terms of set functions .
Page 335
It will first be shown that W satisfies the hypothesis of Zorn's lemma . To do this we let W , be a totally ordered subset of W ( I.22 ) and let c CUW .. Then , for some a e Wo , cna is not void . Let æ be the smallest element of cna ...
It will first be shown that W satisfies the hypothesis of Zorn's lemma . To do this we let W , be a totally ordered subset of W ( I.22 ) and let c CUW .. Then , for some a e Wo , cna is not void . Let æ be the smallest element of cna ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
quences | 26 |
Copyright | |
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Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero