  It is well known that besides oscillations, sequences bounded only in $L^1$
can also develop concentrations, and if the latter occurs, we can at most hope
for weak$^*$ convergence in the sense of measures. Here we derive a new tool to
handle mutual interferences of an oscillating and concentrating sequence with
another weakly converging sequence. We introduce a couple of explicit examples
showing a variety of possible kinds of behavior and outline some applications
in Sobolev spaces.
