Lebesgue-Radon-Nikodym theorem with respect to q-Volkenborn distribution on μq

The purpose of this paper is to derive the analogue of the Lebesgue-Radon-Nikodym theorem with respect to p-adic q-invariant distribution on Zp which is defined by author in Kim (2002) [T. Kim, q-Volkenborn integration, Russian J. Math. Phys. 9 (2002) 288-299].