Alireza Bagheri Salec - Department of Mathematics, Faculty of Basic Science, University of Qom, P.O.Box ۳۷۱۶۱۴۶۶۱۱, Qom, Iran.
Seyyed Mohammad Tabatabaie - Department of Mathematics, Faculty of Basic Science, University of Qom, P.O.Box ۳۷۱۶۱۴۶۶۱۱, Qom, Iran.
Alaa Mahdi Talib Albeka - Department of Mathematics, Faculty of Basic Science, University of Qom, P.O.Box ۳۷۱۶۱۴۶۶۱۱, Qom, Iran.

In this paper we introduce the class of grand Lebesgue spaces associated to a Banach function space X by replacing the role of the L^۱-norm by the norm \|\cdot\|_X in the classical construction of the generalized grand Lebesgue spaces. Also, we study the inclusion property of these spaces.

Grand Lebesgue spaces, Banach function spaces, inclusion, Young function, Orlicz spaces