Radon-Nikodym theorem with respect to $(\rho,q)$-measure on $\Bbb Z_p$

TL;DR

This paper establishes a Radon-Nikodym theorem for the $p$-adic $( ho,q)$-distribution on $Z_p$, extending the framework of $p$-adic analysis with new measure-theoretic results.

Contribution

It introduces a Radon-Nikodym theorem in the context of $p$-adic $( ho,q)$-measures, utilizing Mahler expansion techniques for continuous functions.

Findings

Radon-Nikodym theorem proved for $p$-adic $( ho,q)$-distribution

Extension of $p$-adic measure theory with new measure derivatives

Application of Mahler expansion in $p$-adic measure analysis

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 $\Bbb Z_p$.