Ledrappier-Young formula and exact dimensionality of self-affine measures

作者：Barany Balazs; Kaenmaki Antti^*

来源：Advances in Mathematics, 2017, 318: 88-129.

DOI：10.1016/j.aim.2017.07.015

• Self-affine set
• Self-affine measure
• Hausdorff dimension
• Local dimension

In this paper, we solve the long standing open problem on exact dimensionality of self-affine measures on the plane. We show that every self-affuae measure on the plane is exact dimensional regardless of the choice of the defining iterated function system. In higher dimensions, under certain assumptions, we prove that self-affme and quasi self-affine measures are exact dimensional. In both cases, the measures satisfy the Ledrappier-Young formula.

• 出版日期2017-10-1