For a compact surface \(X_0\), Thurston introduced a compactification of its Teichmüller space \({\mathcal {T}}(X_0)\) by completing it with a boundary \(\mathcal {PML}(X_0)\) consisting of projective measured geodesic laminations. We introduce a similar bordification for the Teichmüller space \({\mathcal {T}}(X_0)\) of a noncompact Riemann surface \(X_0\), using the technical tool of geodesic currents. The lack of compactness requires the introduction of certain uniformity conditions which were unnecessary for compact surfaces. A technical step, providing a convergence result for earthquake paths in \({\mathcal {T}}(X_0)\), may be of independent interest.

对于紧凑的表面\（X_0 \），瑟斯顿引入了边界\（\ mathcal {PML}（X_0）\），从而对其Teichmüller空间\（{\ mathcal {T}}（X_0）\）进行了压缩。由测得的测地线叠层组成。我们使用测地线的技术工具为非紧致黎曼曲面\（X_0 \）的Teichmüller空间\ {{\ mathcal {T}}（X_0）\）引入了相似的化名。缺乏致密性需要引入某些均匀性条件，这对于致密表面而言是不必要的。为\（{\ mathcal {T}}（X_0）\）中的地震路径提供收敛结果的技术步骤可能与您无关。