Independence, sequence entropy and mean sensitivity for invariant measures

Abstract: We investigate the connections between independence, sequence entropy, and mean sensitivity for a measure preserving system under the action of a countable infinite discrete group. We establish that every sequence entropy tuple for an invariant measure is an IT tuple. Furthermore, if the acting group is amenable, we show that for an ergodic measure, the sequence entropy tuples, the mean sensitive tuples along some tempered F{\o}lner sequence, and the sensitive in the mean tuples along some tempered F{\o}lner sequence coincide.