Whether a filtration satisfies the usual conditions depends on the class of null sets and hence the probability measure involved matters. Suppose   satisfies the usual conditions with respect to P, H...

Whether a filtration satisfies the usual conditions depends on the class of null sets and hence the probability measure involved matters. Suppose
  satisfies the usual conditions with respect to P, H is a bounded predictable process, W a Brownian motion with respect to P, M defined by (13.3), and Q defined by If
  if and only if Q(A) = 0.