  Araci et al. introduced a $p$-adic $(\rho,q)$-analogue of the Haar
distribution. By means of the distribution, they constructed the $p$-adic
$(\rho,q)$-Volkenborn integral. In this paper, by virtue of the Mahler
expansion of continuous functions, the author gives the Radon-Nikodym theorem
with respect to the $p$-adic $(\rho,q)$-distribution on $\Bbb Z_p$.
