因子码下测度的重数与类度连接
Multiplicity of measures under factor codes and class degree joinings
摘要：
给定不可约sofic移位之间的有限对一因子码$π: X \to Y$和具有完全支持的$Y$上的遍历$ν$，已知纤维$π^{-1}_*(ν)$在其中至多具有$d_π$遍历测度，其中$d_π$是$π$的次数。我们引入了$X$上遍历测度的重数的概念（这依赖于$π$），并证明了$d_π$是$μ$的重数之和，其中$μ$运行在$π^{-1}_*(ν)$中的遍历测度上.我们还建立了一个适当的推广到无限到一个因子码的类度和相对最大的措施。我们还定义了度连接（有限对一因子码）和类度连接（无限对一因子码）的概念，这是建立我们结果的主要工具
英文摘要：
Given a finite-to-one factor code $π: X \to Y$ between irreducible sofic shifts and an ergodic $ν$ on $Y$ with full support, it is known that the fiber $π^{-1}_*(ν)$ has at most $d_π$ ergodic measures in it where $d_π$ is the degree of $π$. We introduce the notion of multiplicity for ergodic measures on $X$ (that depends on $π$) and we prove that $d_π$ is the sum of the multiplicity of $μ$ where $μ$ runs over the ergodic measures in $π^{-1}_*(ν)$. We also build an appropriate generalization to infinite-to-one factor codes in relation to class degree and relatively maximal measures. We also define the notion of degree joining (for finite-to-one factor codes) and class degree joining (for infinite-to-one factor codes) which are the main tool for establishing our results
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
