=+20.19. Let A ,., (€) = [IZ, - Z|<€, n ≤ k ≤m]. Show that Z ,, - Z with probability 1 if and only if lim ,, lim ,, P(A ,.. (€)) = 1 for all positive

e, whereas Z ,, - +p Z if and only if lim ,, P( A ,,., (€)) = 1 for all positive €.