In this lecture, we will investigate the weighted topological pressure, weighted measure-theoretic entropy and variational principle. Topological pressure is an important topic since these works of Ruelle, Walters and so on.

Following Pesin-Pistskel's definition of topological pressure of non-compact subsets, which resembles the Hausdorff dimension, Feng and Huang introduced weighted topological pressure for Z-action and obtained a variational principle of weighted topological pressure. There is a natural question how to generalize their result to general group action.

We will consider the Z^d-actions.