Tangent Measures of Homogeneous Cantor Sets Satisfying the Strong Separation Condition

Abstract

This paper investigates tangent measures in the sense of Preiss for homogeneous Cantor sets on ℝ^d generated by specific iterated function systems that satisfy the strong separation condition. Through the dynamics of “zooming in” on typical point, we derive an explicit and uniform formula for the tangent measures associated with this category of homogeneous Cantor sets on ℝ^d.