Posterior consistency for semi-parametric regression problems

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Bayesian Estimation of the Spectral Density of a Time Series (2004, methodology): “Further, the result of Amewou-Atisso et al. (2003) is tailor-made for regression and semiparametric problems, in which only weak consistency for the nonparametric part is usually sufficient.”
Dirichlet Process Mixtures of Generalized Linear Models (2009, methodology): “Condition ( i ) is quite hard to show, but there has been recent work demonstrating weak consistency for a number of Dirichlet process mixture models and priors (Ghosal et al. 1999, Ghosh and Ramamoorthi 2003, Amewou-Atisso et al. 2003, Tokdar 2006).”
Remarks on consistency of posterior distributions (2008, background): “7 and show that the Doobtype theorem holds with an assumption on the fixed non-random design points, similar to that of [1].”
Posterior Consistency of Bayesian Quantile Regression Based on the Misspecified Asymmetric Laplace Density (2013, unknown): “Such a condition is used by Amewou-Atisso et al. (2003). It so happens that we need a combination of the above two types of assumptions.”