Normed convergence property for hypergroups admitting an invariant measure (Q1396740)

Let \(K\) be a locally compact hypergroup and \(\mathcal P(K)\) be the space of all probability measures on \(K\) equipped with the weak topology. A hypergroup \(K\) is said to have the normed convergence property if for any sequence \(\{ \mu_n\} \subset \mathcal P(K)\) there exists a sequence \(\{ x_n\} \subset K\) such that the sequence \(\delta_{x_n}*(\mu_1*\cdots *\mu_n)\) is relatively compact. The author proves that for a hypergroup \(K\) admitting a countable basis and an invariant Haar measure the normed convergence property is equivalent to the compactness of \(K\).