We show the existence of generalized compensation functions for a particular type of one-block factor maps π:X → Y between countable subshifts X and Y. For factor maps between compact spaces, continuous compensation functions were studied by Walters in relation to the theory of relative pressure. Applying the thermodynamic formalism for sequences on countable subshifts, we generalize some existing results on factor maps between compact spaces to non-compact spaces. For related questions, we also study the existence of a preimage measure on X of an invariant measure on Y, and their relations.

中文翻译：

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关于可数字母上移位空间之间因子映射的广义补偿函数

我们展示了针对特定类型的单块因子映射的广义补偿函数的存在π：X → 是可数子班次之间X和是. 对于紧致空间之间的因子映射，Walters 研究了与相对压力理论相关的连续补偿函数。将热力学形式应用于可数子位移上的序列，我们将一些现有结果推广到紧致空间与非紧致空间之间的因子映射。对于相关问题，我们还研究了原像测量的存在X的不变测度是，以及它们的关系。