# Questions tagged [fractal-analysis]

Fractal analysis involves the study measures on fractals and their applications. This includes the study of self-similar integration and differential equations on fractals.

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### Does uniform distribution over the Sierpinsky triangle exist?

I'm learning measure theory, I'll make some statements I'm not very sure about. Please correct me if I'm wrong. This problem from a job ad states: Let $(X_1,X_2)$ be uniform over the unit ...
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### Derivative of recursively defined fractal function

I have recently defined a function on the unit interval $[0,1]$ recursively. The definition is based on repeated subdivision of the interval in two equally-sized parts. The definition is as follows: ...
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### Covariance matrix of uniform distribution over the Sierpinski triangle

Let $(X_1, X_2)$ be uniform over the unit Sierpinski triangle (represented in Cartesian coordinates). What is its covariance matrix? This is a question I saw in a jobs ad. I would love some leads on ...
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### Show that this mass distribution measure on the middle-third Cantor set satisfies this identity

For a mass distribution $\mu$ defined on the middle-third Cantor set (with left intervals $E_1$ assigned mass $P_1$ and right intervals masses of $P_2$ with the ratios kept this way throughout the ...
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### A question involving decimal expansions

Let $E_k$ denote those numbers in $[0, 1]$ whose decimal expansions do not contain the digit 5 in the first $k$ decimal places. Can someone explain me why $E_k$ may be regarded as a union of $9^k$ ...