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In this study, for double set sequences, we present the notions of Wijsman asymptotic lacunary invariant equivalence, Wijsman asymptotic lacunary I_2-invariant equivalence and Wijsman asymptotic lacunary I_2^*-invariant equivalence. Also, we examine the relations between these notions and Wijsman asymptotic lacunary invariant statistical equivalence studied in this field before.doi:10.21203/rs.3.rs-548629/v1 fatcat:gkpsdg33orf7fie2p55x3uospq