  In [Mor], we have introduced a notion of flat laminations on surfaces endowed
with a flat structure, similar to geodesic laminations on hyperbolic surfaces.
Here is a sequel to this article that aims at defining transversal measures on
flat laminations similar to transversal measures on hyperbolic laminations,
taking into account that two different leaves of a flat lamination may no
longer disjoint. Then, we define a topology on the set of measured flat
laminations and show that its projective space is compact. Finally, we define
the dual tree to a measured flat lamination.
