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We consider integral functionals ▫${\mathcal F}^{(j)}_{\varepsilon }$▫, doubly indexed by ▫$\varepsilon > 0$▫ and ▫$j \in {\mathbb N}\cup \{ \infty \}$▫, satisfying a standard linear growth condition. We investigate the question of ▫$\Gamma$▫-closure, i.e., when the ▫$\Gamma$▫-convergence of all fam ...