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We introduce a technique that uses projection properties of fractal percolation to establish dimension conservation results for sections of deterministic self-similar sets. For example, let $K$ be a self-similar subset of ${\BBR}^2$ with Hausdorff dimension $\dim _H K \gt 1$ such that the rotational components of the underlying similarities generate the full rotation group. Then, for all $\epsilon...

Dimension Conservation for Self-Similar Sets and Fractal Percolation