An analogue of Lebesgue-Radon-Nikodym theorem with respect to p-adic q-invariant distribution on $\Bbb Z_p$

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The purpose of this paper is to derive the analogue of Lebesgue-Radon-Nikodym theorem with respect to $p$-adic $q$-invariant distribution on $\Bbb Z_p$ which is defined by author in [1].
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