On asymptotically equivalence in sequences of sets

This thesis consists of four main parts. The first part is devoted to the introduction part that contains of the historical development of the subject and a general literature about it. In the second part, the basic concepts necessary for our work are given. In the third part, the concept of asymptotically equivalence of sequences of sets in Wijsman sense is introduced and the relationships between them are given. In the fourth part, by using the I ideal for sequences of sets, Wijsman asymptotic 𝐼-equivalence, Wijsman asymptotically 𝐼-Cesaro equivalence, Wijsman asymptotically I-statistical equivalence and Wijsman asymptotically I_λ-statistical equivalence concepts, their distinctive properties and relationships between these concepts are given.