Show that if S1,..., Sn are predictable stopping times, then so are If At is a predictable process with paths that are right continuous with left limits and a > 0, show is a predictable stopping...

Show that if S₁,..., S_n
are predictable stopping times, then so are

If At is a predictable process with paths that are right continuous with left limits and a > 0, show

is a predictable stopping time.

Show that if T is a predictable stopping time,

is defined to be equal to T (ω) if ω ∈ B and equal to ∞ otherwise, then TB is a predictable stopping time.