Prove Theorem 2.5.1 for the case of an n-dimensional sample space. [The condition that the cumulative distribution function is nondecreasing is replaced by P{x1 < X1 ≤ x

1,...,xn < Xn ≤ x

n} ≥ 0; the condition that it is continuous on the right can be stated as limm→∞ F(x1 + 1/m, . . . , xn + 1/m) =

F(x1,...,xn).]