Martingale - monotone class theorem

Hello,

I want to show by using a monotone class argument that the following equality (i.e. it is a martingale) holds for all bounded and -measurable random variables :

, . (*)

where is an Brownian motion (and it follows from (*) also a Brownian motion).

is the enlargement of the filtration by the filtration generated by a r.v. . So far I have shown that

(*) holds for where is bounded and measurable; and is bounded and -measurable. Now, I think I need a monotone class argument in order to show that (*) holds for all bounded and -measurbale random variables.

But unfortunately I am not very familiar in using monotone class arguments.

How do I find the sets needed in the monotone class theorem?

Thanks in advance.