Show that any process t with independent increments such that E{ } = 0 for

Show that any process ξ_t with independent increments such that E{ξ_Δ} = 0 for any interval Δ, is a martingale. Consider, as an example, w_t. Explain why the assertion of this exercise is formally more general than the assertion of Example 2.1-1 (though it is very close).