On the limit as s → 1- of possibly non-separable fractional Orlicz–Sobolev spaces

Extended versions of the Bourgain–Brezis–Mironescu theorems on the limit as s → 1- of the Gagliardo–Slobodeckij fractional seminorm are established in the Orlicz space setting. Our results hold for fractional Orlicz–Sobolev spaces built upon general Young functions, and complement earlier contributions, where Young functions satisfying the Delta_2 and the Nabla_2 conditions are dealt with. The case of Young functions with an asymptotic linear growth is also considered in connection with the space of functions of bounded variation.