The low of the iterated logarithm for empirical processes under absolute regularity

The compact law of the iterated logarithm for empirical processes whose underlying sequence satisfies a -mixing condition is considered. In particular, we show a compact law of the iterated logarithm for VC subgraph classes of functions, for classes of functions which satisfy the bracketing condition in Doukhanet al. ⁽⁶⁾ and for some classes of smooth functions.Research partially supported by NSF Grant DMS-93-02583.