soxumis saxelmwifo universitetis S r o m e b i VII

1n24nj121a1 j Ftj Kg1u hThereforea10u t2h 1 hdu 1a2 u t h 1 nhFtdt K g u du O .1a1a2 21 u t 1 2 1 n F t dt Kg1u du n n O2 , (27) h h nhaa1n2na011a22 1 ha1a u t h 1Ftdt K g u du ,2 1 ha1aSince by F u1 Fu , u c8 u t h 1Ftdt K g u du .14ag andFu 1 , a u aF1 ,it follows that1u c9a1 F1 ag , we have1at a h 1n c10dt Kudu, (28)0 at h where a t 0 and 1at 0. The first inequality is obvious,whereas the second one follows from the inequalities 0 t a and10 a .2Therefore1ath 0,0 t a,lim Kudu 1n at , t a.h2By the Lebesgue theorem on bounded convergence, from the latterexpression and (28) we obtain1 0 as n . (29)n212222