{"paper":{"title":"Dimension conservation for self-similar sets and fractal percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Kenneth Falconer, Xiong Jin","submitted_at":"2014-09-05T17:34:04Z","abstract_excerpt":"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 $\\mathbb{R}^2$ with Hausdorff dimension $\\dim_H K >1$ such that the rotational components of the underlying similarities generate the full rotation group. Then for all $\\epsilon >0$, writing $\\pi_\\theta$ for projection onto the line $L_\\theta$ in direction $\\theta$, the Hausdorff dimensions of the sections satisfy $\\dim_H (K\\cap \\pi_\\theta^{-1}x)> \\dim_H K - 1 - \\epsilon$ for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1882","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}