We establish that Laplace transforms of the posterior Dirichlet process converge to those of the limiting Brownian bridge process in a neighbourhood about zero, uniformly over Glivenko-Cantelli function classes. For real-valued random variables and functions of bounded variation, we strengthen this result to hold for all real numbers. This last result is proved via an explicit strong approximation coupling inequality.

翻译：我们确认,拉普尔(Laplace)的后置Drichlet进程转换与限制布朗桥进程的转变相趋同,位于一个大约零点的街区,统一在Glivenko-Cantelli功能等级上。 对于实际价值随机变量和约束变量的功能,我们强化了这一结果,以维持所有真实数字。 最后一个结果是通过明显的强烈近似近距离的不平等来证明的。