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This question was previously posted on MSE. Let $K\subset \mathbb R^2$ be a compact fractal of Hausdorff dimension $1<d<2$. I want to define a natural measure on $K$. One option would be to use ...

This is my first time to ask a question here. Please tell me if I can improve it. I would like to introduce the following definition inspired from a measure theory exercise. Definition. A subset $K$ ...