Let (E, ) be a metric space and let hE (5) be the cardinality of the set of 5-connected components of E. In literature, in case of that E is a self-conformal set satisfying the open set condition or E is a self-affine Sierpinski sponge, necessary and sufficient condition is given for the validity of the relation hE(5) x 5- dimB E, when 5 & RARR; 0. In this paper, we generalize the above result to self-affine sponges of LalleyGatzouras type; actually in this case, we show that there exists a Bernoulli measure & mu; such that for any cylinder W...
