It is well known that the open set condition and the positivity of the t-dimensional Hausdorff measure are equivalent on self-similar sets, where t is the zero of the topological pressure. We prove an analogous result for a class of Moran constructions and we study different kinds of Moran constructions in this respect.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm200-1-2,
author = {Antti K\"aenm\"aki and Markku Vilppolainen},
title = {Separation conditions on controlled Moran constructions},
journal = {Fundamenta Mathematicae},
volume = {201},
year = {2008},
pages = {69-100},
zbl = {1148.28007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm200-1-2}
}
Antti Käenmäki; Markku Vilppolainen. Separation conditions on controlled Moran constructions. Fundamenta Mathematicae, Tome 201 (2008) pp. 69-100. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm200-1-2/