Abstract
In this paper we define ?-independent (a weak-version of independence), Kronecker and dissociate sets on hypergroups and study their properties and relationships among them and some other thin sets such as independent and Sidon sets. These sets have the lacunarity or thinness property and are very useful indeed. For example Varopoulos used the Kronecker sets to prove the Malliavin theorem. In the final section we bring some examples and find ?-independent and dissociate sets on a compact countable hypergroup of Dunkle and Ramirez, the dual Chebychev polynomial hypergroup, and some other polynomial hypergroups from Lasser.
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