Local pressure of subsets and measures (Q2060005)

The author considers and generalizes many properties of the local metric pressure and the local metric lower and upper capacities with respect to a fixed open cover, which are defined by the Carathéodory-Pesin construction. In particular, all local pressures of an ergodic measure are verified to be equal to the local metric entropy plus the integral of the potential up to a variation of the potential itself with respect to the open cover. This answers positively a question by \textit{T. Downarowicz} [Entropy in dynamical systems. Cambridge: Cambridge University Press (2011; Zbl 1220.37001)] on variant entropy.