On one hand we have )=A(1/)=klog(1/) On the other hand HSO )sH1p,…P)+;Hm1/n,…1m) n i=1 Hs(P1,…,队+k-1p;log Hence H(P,…,R)=kg(/)1;P吗 n 1P0g早 0 (c)If p are irrational, the equation also valid, see (1)On one hand we have H ( … ) = A(1/ ) = k log (1/ ) On the other hand H ( … ) = H (p , …, p ) + p H (1/n , …, 1/n ) = H (p , …, p ) + A(n ) = H (p , …, p ) + k log n 1 N i i i N i=1 S S S S S 1 N i=1 N p i i=1 N p i S 1 N Hence H (p , …, p ) = k[log(1/ ) - p log n ] = - k p log n = - k p log p i i i=1 N i i i=1 N i=1 N i i i i 1 N (c) If p are irrational, the equation also valid, see (1). S