A New Mixing Condition

In this paper a new mixing condition for sequences of random variables is considered. This mixing condition is termed γ-mixing. Whereas mixing conditions such as α-mixing are typically defined in terms of entire σ-fields of sets generated by random variables in the distant past and future, γ-mixing is defined in terms of a smaller class of sets: the finite dimensional cylinder sets. This leads to a definition of mixing more general than those in current use. A Rosenthal inequality, law of large numbers, and functional central limit theorem are proved for γ-mixing processes.