This paper considers functional central limit theorems for stationary absolutely regular
mixing processes. Bounds for the entropy with bracketing are derived using recent results
in Nickl and Pötscher (2007). More specifically, their bracketing metric entropy bounds
are extended to a norm defined in Doukhan, Massart and Rio (1995, henceforth DMR) that
depends both on the marginal distribution of the process and on the mixing coefficients.
Using these bounds, and based on a result in DMR, it is shown that for the class of weighted