Dimension and measures on sub-self-affine sets (Q711625)

The authors study the dimension of a typical so-called sub-self-affine set which extends the self-affine set from the classical case studied by J. Hutchinson, K. J. Falconer and others. In Theorem 5.2 the same result for a typical sub-self-affine set is proved and further, that such a set carries an invariant measure of full Hausdorff dimension as obtained by Falconer for sub-self-similar sets satisfying the open set condition. The proof of Theorem 5.2 is based on the existence of an equilibrium measure (Section 3). The authors study in section 4 some properties of the topological pressure (Theorem 4.4). The paper is well written and the subject is a very current one. It answers a question of Falconer.