  An invariant measure for a flow is, of course, an invariant measure for any
of its time-t maps. But the converse is far from being true. Hence, one may
naturally ask: What is the obstruction for an invariant measure for the
time-one map to be invariant for the flow itself? We give an answer in terms of
measure disintegration. Surprisingly all it takes is the measure not to be "too
much pathological in the orbits". We prove the following rigidity result. If
$\mu$ is an ergodic probability for the time-one map of a flow, then it is
either highly pathological in the orbits, or it is highly regular (i.e
invariant for the flow). In particular this measure rigidity result is also
true for measurable flows by the classical Ambrose-Kakutani's representation
theorem for measurable flows.
