Abstract
Based on several types of weighted sub-additive topological pressures which arise from the theory of Carathéodory structure, we define various weighted sub-additive measure-theoretic pressures. Also, a characterization of weighted sub-additive measure-theoretic pressures for ergodic measures is derived in terms of weighted measure-theoretic entropy, which immediately indicates an inverse variational principle for weighted sub-additive topological pressure. Afterward we illustrate that the inverse variational principle can be attained on the set of generic points of the ergodic measure μ when the potential is additive.
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