A Note on the Lebesgue-Radon-Nikodym Theorem with respect to Weighted p -adic Invariant Integral on ℤ p

Abstract

We will give the Lebesgue-Radon-Nikodym theorem with respect to weighted $p$-adic $q$-measure on ${\mathbb{Z}}_p$. In special case, $q=1$, we can derive the same result as Kim, 2012; Kim et al., 2011.