A well known theorem of Thurston asserts the existence of a homeomorphism between the spaces of measured foliations and of measured laminations of any hyperbolic surface. Where can I find a construction of this homeomorphism?
I am aware that the epilogue of Penner-Harer "Combinatorics of Train Tracks" mentions that a measured train track $(\tau,\mu)$ gives rise to both a measured foliation and to a measured lamination, however it seems to me that this is not enough for the definition of a homeomorphism since for example such $(\tau,\mu)$ is not unique for a given measured foliation or lamination. Also, one needs to be careful about Whitehead equivalence.
A web search produced this account of that theorem, written up by Kashyap Rajeevsarathy.