The Simplest Tauberian Theorem.

The following problem is considered: obtain the asymptotic properties of a function <MATH>u</MATH> from the asymptotic properties of the integral <MATH>\int_0^r{u(t)}\,dt</MATH>. As is well known, this can be done under additional constraints on the function <MATH>u(t)</MATH>. In this paper, we obtain a theorem in which these constraints are weaker than in other well-known versions of such theorems. [ABSTRACT FROM AUTHOR]