Suppose Mo, M,..., MN is a martingale, and let A0, A, AN-1 be an adapted stochas- tic process. Define the discrete-time stochastic integral (sometimes called a martingale transform) Io, 1,, IN by setting Io = 0 and n-1 In = Aj(Mj+1-M), n = 1,..., N. j=1 Show that Io, 11,..., IN is a martingale.