Radon-Nikodym theorem with respect to $(\rho ,q)$-measure on ${\mathbb{Z}}_p$

Abstract

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 ${\mathbb{Z}}_p$.