Abstract:
 Without any additional conditions on subadditive potentials, this talk defines subadditive measuretheoretic pressure, and shows that the subadditive measuretheoretic pressure for ergodic measures can be described in terms of measuretheoretic entropy and an constant associated with the ergodic measure. Based on the definition of topological pressure on noncompact set, we give another equivalent definition of subadditive measuretheoretic pressure, and we can obtain an inverse variational principle. This paper also studies the superadditive measuretheoretic pressure which has similar formalism as the subadditive measuretheoretic pressure. Moreover, we prove that the zero of the nonadditive measuretheoretic pressure gives the lower and upper bound estimate of dimensions of an ergodic measure.
