论文标题
金曼的亚脱贡定理的泛化
A gapped generalization of Kingman's subadditive ergodic theorem
论文作者
论文摘要
我们指出并证明了金曼对措施的动力学系统$（x，\ mathcal {f}，μ，μ，t）$的概括，其中$μ$非常确定的亚加成条件$ f_ {n + m} \ leq f_n + leq f_n + f_n + f_n + f_m \ cird circe niws nive nive nive nive nive nised nive nised n n and papper表格$ f_ {n+σ_m+m} \ leq f_n+ρ_n+f_m \ circt t^{n+σ_n} $的子添加条件，用于某些非否中的$ρ_n\ in L^1（\ a \ {0 \} $在$ n $中适当地sublinear。这种概括对单方面偏移的适当脱钩度量的特定相对熵的存在首次应用。
We state and prove a generalization of Kingman's ergodic theorem on a measure-preserving dynamical system $(X,\mathcal{F},μ,T)$ where the $μ$-almost sure subadditivity condition $f_{n+m} \leq f_n + f_m \circ T^{n}$ is relaxed to a $μ$-almost sure, "gapped", almost subadditivity condition of the form $f_{n+σ_m+m} \leq f_n +ρ_n + f_m \circ T^{n+σ_n}$ for some nonnegative $ρ_n \in L^1(\mathrm{d}μ)$ and $σ_n \in \mathbf{N} \cup \{0\}$ that are suitably sublinear in $n$. This generalization has a first application to the existence of specific relative entropies for suitably decoupled measures on one-sided shifts.
