Likelihood ratio for densities with singularity

Let $t_n$ be Bayes estimate of parameter $\Theta$. The case of independent observations with infinite information quantity is considered. Under some conditions on densities it is shown that normalizing factor $\varphi(n)$ for $\Delta_n\varphi(n)(t_n-\Theta)$ to have nontrivial asymptotic destribution is regularly changing in the sence of Karamata. Asymptotic distribution of $\Delta_n$ derived.