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Page 269
Since the integral [ st ( s ) u ( ds ) satisfies the inequality IJsH ( 9 ) u ( ds ) ) = sup | t ( s ) vlu , S ) , it is clear that the integral is a continuous linear functional on C ( $ ) . The following theorem is a converse to this ...
Since the integral [ st ( s ) u ( ds ) satisfies the inequality IJsH ( 9 ) u ( ds ) ) = sup | t ( s ) vlu , S ) , it is clear that the integral is a continuous linear functional on C ( $ ) . The following theorem is a converse to this ...
Page 282
It is clear that T ( 8 ) CT ( d ) if € < d and that -te T ( E ) whenever te T ( E ) . The function f is said to be almost periodic if it is continuous and if for every e > 0 there is an L L ( 8 ) > 0 such that every interval in R of ...
It is clear that T ( 8 ) CT ( d ) if € < d and that -te T ( E ) whenever te T ( E ) . The function f is said to be almost periodic if it is continuous and if for every e > 0 there is an L L ( 8 ) > 0 such that every interval in R of ...
Page 292
It is clear that if F , and F , are elements of E3 , then F F , € Eg . It is also clear that if F , € Ez , then S - F , € Ez , and that if F1 , F2 € Eg with F , F2 = $ , then Fi UF , € Eg . It follows that E , is a field .
It is clear that if F , and F , are elements of E3 , then F F , € Eg . It is also clear that if F , € Ez , then S - F , € Ez , and that if F1 , F2 € Eg with F , F2 = $ , then Fi UF , € Eg . It follows that E , is a field .
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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