  We introduce the notion of metric entropy for a nonautonomous dynamical
system given by a sequence of probability spaces and a sequence of
measure-preserving maps between these spaces. This notion generalizes the
classical concept of metric entropy established by Kolmogorov and Sinai, and is
related via a variational inequality to the topological entropy of
nonautonomous systems as defined by Kolyada, Misiurewicz and Snoha. Moreover,
it shares several properties with the classical notion of metric entropy. In
particular, invariance with respect to appropriately defined isomorphisms, a
power rule, and a Rokhlin-type inequality are proved.
