  Yurova \cite{Yu} and Anashin et al. \cite{AKY1, AKY2} characterize the
ergodicity of a 1-Lipschitz function on $\Z_2$ in terms of the van der Put
expansion. Motivated by their recent work, we provide the sufficient conditions
for the ergodicity of such a function defined on a more general setting $\Z_p$.
  In addition, we provide alternative proofs of two criteria (because of
\cite{AKY1, AKY2} and \cite{Yu}) for an ergodic 1-Lipschitz function on $\Z_2,$
represented by both the Mahler basis and the van der Put basis.
