Measurable selections of limit points (Q1088016)

The main purpose of this paper is to prove the existence of a Borel measurable selection of limit points in a dual Banach space not necessarily separable and equipped with the weak star topology. In order to do that the author first establishes some auxiliary results in a very general context, some of which of independent interest. The main theorem contains an earlier result given by \textit{A. D. Kuz'min} [Vestn. Mosk. Univ., Ser. XV 1977, No.2, 58-66 (1977; Zbl 0436.62011)] concerning the existence of a Borel measurable selection of limit points in a separable Hilbert space equipped with the weak topology.