# Construction of a set of p-adic distributions

## TL;DR

This paper develops methods to construct $p$-adic distributions on $Z_p$, adapting real-valued Gibbs measure techniques, and identifies conditions for these distributions to be bounded measures.

## Contribution

It introduces a novel approach to constructing $p$-adic distributions on $Z_p$ inspired by Gibbs measures on Cayley trees, extending existing methods.

## Key findings

- Constructed several $p$-adic distributions on $Z_p$
- Provided conditions for these distributions to be $p$-adic measures
- Extended real-valued Gibbs measure techniques to the $p$-adic setting

## Abstract

In this paper adapting to $p$-adic case some methods of real valued Gibbs measures on Cayley trees we construct several $p$-adic distributions on the set $\mathbb{Z}_p$ of $p$-adic integers. Moreover, we give conditions under which these $p$-adic distributions become $p$-adic measures (i.e. bounded distributions).