论文标题
扩展手段的不变性财产
Invariance property for extended means
论文作者
论文摘要
e研究均值型映射的属性$ {\ bf m} \ cOLON i^p \ to i^p $ m}（x_1，\ dots，x_p）：= \ big（m_1（x_ {α_{α_{1,1}}}，\ dots，x__ {α__{1，d _1}}），\ dots，m_p（x_ {α_{p，1}}，\ dots，x_ {α_{p，d_p}}）\ big），$$其中$ p $和$ d_i $ -s是积极的整数，每个$ m_i $都是$ d_i $ - 可变性的平均值，而间隔$ i \ subset \ subset \ mathbb {r} $和$α_{i，j} $ - s是$ \ \ dots，p \ p \ f \ \ \} $的元素。 我们表明，在$ m_i $ -s上的一些自然假设下，现有的问题可以将唯一的$ \ bf m $ - invariant均值减少到带有顶点图的刻度性，并用顶点$ \ {1，\ dots，p \}，p \}，p \ _允许} \} $。
e study the properties of the mean-type mappings ${\bf M}\colon I^p \to I^p$ of the form $${\bf M}(x_1,\dots,x_p):=\big(M_1(x_{α_{1,1}},\dots,x_{α_{1,d_1}}),\dots,M_p(x_{α_{p,1}},\dots,x_{α_{p,d_p}})\big),$$ where $p$ and $d_i$-s are positive integers, each $M_i$ is a $d_i$-variable mean on an interval $I \subset \mathbb{R}$, and $α_{i,j}$-s are elements from $\{1,\dots,p\}$. We show that, under some natural assumption on $M_i$-s, the problem of existing the unique $\bf M$-invariant mean can be reduced to the ergodicity of the directed graph with vertexes $\{1,\dots,p\}$ and edges $\{(α_{i,j},i) \colon i,j \text{ admissible}\}$.
