Resumen de The µ-topological Hausdorff dimensio

Hela Lotfi

• : In 2015, R. Balkaa, Z. Buczolich and M. Elekes introduced the topological Hausdorff dimension which is a combination of the definitions of the topological dimension and the Hausdorff dimension. In our manuscript, we propose to generalize the topological Hausdorff dimension by combining the definitions of the topological dimension and the µ-Hausdorff dimension and we call it the µ-topological Hausdorff dimension. We will present upper and lower bounds for the µ-topological Hausdorff dimension of the Sierpi´nski carpet valid in a general framework. As an application, we give a large class of measures µ, where the µ-topological Hausdorff dimension of the Sierpi´nski carpet coincides with the lower and upper bounds