Let the r.v.s X n , n ³ 1, be defined as follows : X n (w) = 2 n if w à (0, 1/

Let the r.v.sX_n,n³ 1, be defined as follows :X_n(w) =2ⁿif w ÃŽ (0, 1/n), andX_n(w) = 0 otherwise, where (W,A,P) = ((0, 1], B(0, 1], l) and l is the Lebesgue measure. Then show that

pointwise, but

To any finite number for any r > 0; in fact

For any r > 0.

Xn 0