Let (Ω, F, P)=([0, 1], [0, 1], μ)N (μ is the Lebesque measure, N={1, 2,…}).{Xn}n=1∞ are independent random variables on (Ω, F, P) with Xn(ω)=ωn, where ω=(ω1, ω2,…). The {Xn}n=1∞ are almost surely distinct. Thus to almost all sample points ω there is a random partial order 【 of the integers given by