TANGENT MEASURES ON HOMOGENEOUS CANTOR SETS ON ℝ SATISFYING THE CONVEX OPEN SET CONDITION

This paper investigates tangent measures in the sense of Preiss for homogeneous Cantor sets on [Formula: see text] satisfying the convex open set condition, a similar problem has been discussed in our previous work but with the strong separation condition. Through the dynamics of “zooming in” on any typical point, we derive an explicit and uniform formula for the tangent measures associated with this category of homogeneous Cantor sets on [Formula: see text].