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| e(Yu{ae))dx/ | e(Yu6(x))dx JA JK >lKlç(Vrnlr)*+* d' où I' ,
, Afin de prouver le Théorème 2.I, nous avons besoin des deux lemmes suivants
, (1.7) et (1,8) Alors, si le segment [r,r'] est contenu dans O on a : A; w; . t -r' S G(ae) -G(*') 1v
, On désigne par A l'infimum et par V le supremum)
, Démonstration, issue.25
, Il suffit d'appliquer le théorème des valeurs intermédiaires après régularisation (voir
, Remarque 2.2 : Une conséquence immédiate du Lemme 2.1 est que G(r)-G
, sur chaque segment l*,r'l tel que t-fr' ?Wt, où l7r désigne I'espace orthogonal de W, qui est réduit à zêro lorsque les tl; engendrent tout I'espace
t p une base de W et par r, les points du réseau detaille ho,(ot ? (0,1)serachoisiplusloin)généréparlesu; i.e. pourz : (zrtz2s...,zp) ? lP quelconque on pose ,
,
, Rappelons que VA(r)?Co(w;) p.p.c ?CI (3.4)
, n) tel que ri ? [0, 1] et VA(x)-ta;(n)w; , ta;@):t. (3.5) i:l i=l
, De plus, on sait que ûr est unique grâce au (3.3). en fait, ai(r) est mesurable (voir I C
, On rappelle un Théorème qui est bien-connu ( voir pax exemple
, Lemme 3
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