Measure-preserving and ergodic an n-unit delay mappings

The automaton transformation of infinite words over alphabet $F_p={0,1,..,p-1}$, where $p$ prime number coincide with continuous transformation of a ring of p-adic integers $Z_p$. The object of this study is the an $n$-unit delay maps (associated with asynchronous automata) that is important for cryptography. We prove criteria of measure-preserving for an n-unit delay mappings. Moreover, we give a sufficient condition of ergodicity of such mappings.