Let (X n , F n ) n=1,2,. ,N be a martingale in discrete time and a stopping time with respect to (F n ). Define the collection of events F = { A F :...

Let (Xn, Fn)n=1,2,...,N be a martingale in discrete time and τ a stopping time with respect to (Fn). Define the collection of events Fτ = { A ∈ F : A ∩ {τ ≤ n} ∈ Fn, n = 1, 2, ....}Show that Fτ is a σ-algebra of events in F [i.e., ∅ is in Fτ , and Fτ is closed under complements and countable unions.]