Uniform weak* topology and earthquakes in the hyperbolic plane

We prove that the bijective correspondence between the space of bounded measured laminations ℳℒ b (ℍ) and the universal Teichmüller space T (ℍ) given byλ ↦ E λ |S 1is a homeomorphism for the uniform weak* topology on ℳℒ b (ℍ) and the Teichmüller topology on T (ℍ), where E λ is an earthquake with an earthquake measure λ. A corollary is that earthquakes with discrete earthquake measures are dense in T (ℍ). We also establish infinitesimal versions of the above results.