Abstract
For a family \((\mathscr {A}_x)_{x \in (0,1)}\) of integral quasi-arithmetic means satisfying certain measurability-type assumptions we search for an integral mean K such that \(K\big ((\mathscr {A}_x(\mathbb {P}))_{x \in (0,1)}\big )=K(\mathbb {P})\) for every compactly supported probability Borel measure \(\mathbb {P}\). Also some results concerning the uniqueness of invariant means will be given.
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Deręgowska, B., Pasteczka, P. Quasi-arithmetic-type invariant means on probability space. Aequat. Math. 95, 639–651 (2021). https://doi.org/10.1007/s00010-020-00765-8
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DOI: https://doi.org/10.1007/s00010-020-00765-8