The numbers of level crossings and extremes for random processes and fields play an important role in reliability theory and many engineering applications. In many cases for Gaussian processes the Poisson approximation for their asymptotic distributions is used.
This paper extends an approach proposed in Rusakov and Seleznjev (1988) for smooth random processes on a finite interval. It turns out that a number of functionals (including some integervalued ones) become continuous on the space of smooth functions and weak convergence results for the sequences of such continuous functionals
are applicable. Examples of such functionals for smooth random processes on infinite intervals and for random fields are studied
