| 摘要: | This paper studies the relations between Pesin-Pitskel topological pressure on an arbitrary subset and measure theoretic pressure of Borel probability measures, which extends Feng and Huang's recent result on entropies [13] for pressures. More precisely, this paper defines the measure theoretic pressure P-mu(T, f) for any Borel probability measure, and shows that P-B(T, f, K) = sup{P-mu(T, f) : mu is an element of M(X), (mu)(K) = 1}, where M(X) is the space of all Borel probability measures, K subset of X is a non-empty compact subset and P-B(T, f, K) is the Pesin-Pitskel topological pressure on K. Furthermore, if Z subset of X is an analytic subset, then P-B(T, f, Z) = sup{P-B(T, f, K) K subset of Z is compact}. This paper also shows that Pesin-Pitskel topological pressure can be determined by the measure theoretic pressure. (C) 2014 Elsevier Inc. All rights reserved. |
