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.

中文翻译：

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概率空间上的拟算术类型不变式

对于满足拟度量标准假设的族\（（（mathscr {A} _x）_ {x \ in（0,1）} \），满足某些可测量性类型的假设，我们搜索积分均值K，使得\（K每个紧密支持的概率Borel测度\ big（（（\ mathscr {A} _x（\ mathbb {P}））_ {x \ in（0,1）} \ big）= K（\ mathbb {P}）\）\（\ mathbb {P} \）。还将给出一些关于不变式唯一性的结果。