Hallo,

I have to show that the following sets of stochastic processes are not equal:

is progessive measurable and

is progessive measurable and a.s.

I know that these sets aren't equal.

But how can I show that a.s. doesn't imply

Does anyone know a proof?

I also know that the Itô-integral where is a standard Brownian motion and is not just a local martingale, it's also a martingale.

But is also a martingale if ?

Can anybody help me?

Thanks!