  The paper considers the properties of pseudo stationarity in a broad sense
and pseudo strong mixing for sequences of random variables corresponding to
arithmetic functions. Assertions on this topic have been proven. The
implementation of these properties for known arithmetic functions has been
verified. The article proves a statement about sufficient conditions under
which a summation arithmetic function with bounded terms has a limit normal
distribution law. The fulfillment of the specified sufficient conditions for
known arithmetic functions is considered.
