On the Approximation by Mellin Transform of the Riemann Zeta-Function

This paper is devoted to the approximation of a certain class analytic functions by shifts Z(s+iτ), τ∈R, modified Mellin transform Z(s) square Riemann zeta-function ζ(1/2+it). More precisely, we prove existence closed non-empty set F such that there are infinitely many which approximate given function from with accuracy. In proof, weak convergence measures in space applied. Then, coincides support limit measure.