Lebesque-Radon-Nikodym theorem with respect to p-adic invariant measure on Zp

TL;DR

This paper establishes a p-adic analogue of the Lebesgue-Radon-Nikodym theorem for fermionic invariant measures on Zp, expanding measure theory into the p-adic setting.

Contribution

It introduces a new version of the Lebesgue-Radon-Nikodym theorem tailored for fermionic p-adic invariant measures on Zp, a novel extension in p-adic measure theory.

Findings

Derived the p-adic Lebesgue-Radon-Nikodym theorem for fermionic measures

Extended classical measure theory into the p-adic context

Provided foundational results for p-adic measure analysis

Abstract

In this paper we derive the analogue of Lebesque-Radon Nikody theorem with respect to fermionic p-adic invariant measures on Zp