In this paper, we use some bi-sequences of positive numbers to define weighted dynamical metrics. Then we show that, replacing the Bowen dynamical metric by the weighted metric, the definition of pressure for asymptotically sub-additive potentials, including measure-theoretic and topological, is not affected. This generalizes some known results for pressure, defined using mean metrics and continuous potentials.

Keywords: Asymptotically sub-additive potential, Measure-theoretic pressure, Topological pressure, weighted metric.

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