On properties of sets under certain transformations

Mukul Pal and Santimoy Panda, Kalyani, India

Keywords: N-dimensional Euclidean space, Lebesgue measure, T_{ω} transformation (ω being an element of a metric space), Metric space AMS Subject classification: 28A05

Abstract: In this paper the properties of sets are studied under the transformations of the form T_{ω} (ω being an element of a metric space) as considered by M. Pal in [5]. The paper also deals with the problems on sets of positive Lebesgue measure under the transformations as introduced here. Also the equivalence of one of the conditions of [5] and the condition as introduced here is obtained.