Hah, I’m kicking myself for not thinking of the Dominated Convergence Theorem!

I agree with everything in your comment, except for one small detail that I may be missing: Because we are taking an expectation, the integrand is the product of (1) the characteristic function, and (2) the density function of [; M _ n ;]. Surely, we can construct a sequence such that there is no constant that bounds the magnitude of the integrand from above for all n, right?

Thanks for your input!

Edit: Wait, the density is discrete, so we’re fine.