次可加测度压的一个注记

A Note on the Measure-Theoretic Pressure in Sub-additive Case

利用非紧集上拓扑压的定义,对任意一个不变测度和一族紧度量空间上的次可加势函数,引进了一个新的次可加测度压的定义.在某些假设下,对任意一个遍历测度,证明了新定义的次可加测度压等于用生成集定义的次可加测度压.进一步得到了一个逆变分原理,即次可加测度压等于在某个非紧集上的拓扑压.

By using the definition of topological pressure for non-compact set,a new def- inition of measure-theoretic pressure for invariant measures of sub-additive potentials on a compact metric space is introduced.For any ergodic measure,under some mild assumptions, the author proves that it is equal to the sub-additive measure-theoretic pressure defined by spanning set.Moreover,an inverse variational principle is obtained.Namely,the sub- additive measure-theoretic pressure is equal to the sub-additive topological pressure on a certain set.