Bernstein sets andκ-coverings

䅢stract. In this paper we study a notion of a �-covering in connection with Bernstein sets and other types of nonmeasurability. Our results correspond to those obtained by Muthuvel in [7] and Nowik in [8]. We consider also other types of coverings. 1. Definitions and notation In 1993 Car汳on 楮 h楳 paper 嬳] 楮troduced a not楯n of �-cover楮gs and used 楴 for 楮vest楧at楮g whether some 楤ea汳 are or are not �-trans污tab汥. Later on �-cover楮gs were stud楥d by other authors, e⹧. Muthuvel (cf. [7 崩 and Now楫 (cf. 嬸崬 嬹崩. In th楳 paper we present new resu汴s on �-cover楮gs 楮 connect楯n w楴h Bernste楮 sets. We a汳o 楮troduce two natural genera汩zat楯ns of the not楯n of �-cover楮gs, name汹 �-S-cover楮gs and �-I-cover楮gs. We use …