{"paper":{"title":"Measures of the full Hausdorff dimension for a general Sierpi\\'{n}ski carpet","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Chih-Hung Chang, Jung-Chao Ban, Ting-Ju Chen","submitted_at":"2012-06-06T11:41:03Z","abstract_excerpt":"The measure of the full dimension for a general Sierpi\\'{n}ski carpet is studied. In the first part of this study, we give a criterion for the measure of the full Hausdorff dimension of a Sierpi\\'{n}ski carpet. Meanwhile, it is the conditional equilibrium measure of zero potential with respect to some Gibbs measure $\\nu_{\\alpha}$ of matrix-valued potential $\\alpha\\mathbf{N}$ (defined later). On one hand, this investigation extends the result of [17] without condition \\textbf{(H)}. On the other hand, it provides a checkable condition to ensure the existence and uniqueness of the measure of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1190","kind":"arxiv","version":1},"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"}