MARIUS MANTOIU ON ABELIAN C*-ALGEBRAS WHICH ARE INDEPENDENT WITH RESPECT TO A FILTER (425K, Postscript) ABSTRACT. We examine extensions of the concept of asymptotic independence, introduced in [14] and useful in the study of abelian C*-algebras generated by the union of two of its C*-subalgebras. We give non-trivial examples in terms of classes of bounded, continuous functions defined on a locally compact group. The results are useful in the spectral analysis of Schroedinger-type operators.