Singularity of energy measures on a class of inhomogeneous Sierpinski gaskets

TL;DR

This paper investigates the relationship between energy measures and reference measures on inhomogeneous Sierpinski gaskets, establishing their mutual singularity under certain conditions.

Contribution

It demonstrates the singularity between energy measures and reference measures on inhomogeneous Sierpinski gaskets, advancing understanding of measure interactions on fractals.

Findings

Energy measures are mutually singular with reference measures.

Mutual singularity holds under mild assumptions.

Provides insight into measure behavior on fractal structures.

Abstract

We study energy measures of canonical Dirichlet forms on inhomogeneous Sierpinski gaskets. We prove that the energy measures and suitable reference measures are mutually singular under mild assumptions.