Some Properties of N-Integral on Set-Valued Functions

The Upper and Lower N-integrals were introduced in 2019 based on the concept of δ-fine partitions, which also underlies the Henstock–Kurzweil integral. While the integration of set-valued functions was initially developed through measure-theoretic approaches, later studies extended the Henstock–Kurzweil integral to the set-valued setting and compared it with measure-based integrals. In this paper, we study the N-integral for set-valued functions within this framework. We prove that the N-integral satisfies fundamental properties such as boundedness and linearity, and we establish conditions under which it coincides with the Henstock–Kurzweil integral. Our results extend and complement several earlier results on the integration of set-valued functions and Henstock–Kurzweil-type integrals.