Construction of a set of p-adic distributions

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).