Weak convergence of the adjusted range of cumulative sums of exchangeable random variables

Let R* be the adjusted range of the cumulative sums of a sequence {X,: s = 1,2, }" : R} = max,,,,, (,S1) mini,, (.S*), where ,S* = S,. (Xan-' l .. X,). Weak convergence results for random functions constructed from cumulative sums of {X, } are used to obtain the asympt tic distribution and moments of R * when {X, } are exchangeable, or symmetrically dependent, random variables. FUNCTIONAL CENTRAL LIMIT THEOREM; EXCHANGEABLE SEQUENCES