  We develop a fine-scale local analysis of measure entropy and measure
sequence entropy based on combinatorial independence. The concepts of measure
IE-tuples and measure IN-tuples are introduced and studied in analogy with
their counterparts in topological dynamics. Local characterizations of the
Pinsker von Neumann algebra and its sequence entropy analogue are given in
terms of combinatorial independence, l_1 geometry, and Voiculescu's completely
positive approximation entropy. Among the novel features of our local study is
the treatment of general discrete acting groups, with the structural assumption
of amenability in the case of entropy.
