The Szlenk index of Lp(X)

We find an optimal upper bound on the values of the weak*-dentability index Dz(X) in terms of the Szlenk index Sz(X) of a Banach space X with separable dual. Namely, if Sz(X) =omega(alpha), for some alpha < omega(1), and p epsilon (1,infinity), then Sz(X) <= Dz(X) <= Sz(L-p(X)) <= {omega(alpha+1) if alpha is a finite ordinal, omega(alpha) if alpha is an infinite ordinal.