Let X1, X2,... be independent r.v.s, and let the r.v. X be An = (Xn, Xn+1,.. .)-measurable

Let X1, X2,... be independent r.v.s, and let the r.v. X be An = σ(Xn, Xn+1,.. .)-measurable for every n ≥ 1. Then show that P(X = c) = 1 for some (finite) constant c.