{"paper":{"title":"Projections of planar Mandelbrot measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"De-Jun Feng, Julien Barral","submitted_at":"2016-05-30T01:27:08Z","abstract_excerpt":"Let $\\mu$ be a planar Mandelbrot measure and $\\pi_*\\mu$ its orthogonal projection on one of the main axes. We study the thermodynamic and geometric properties of $\\pi_*\\mu$. We first show that $\\pi_*\\mu$ is exactly dimensional, with $\\dim(\\pi_*\\mu)=\\min(\\dim(\\mu),\\dim(\\nu))$, where~$\\nu$ is the Bernoulli product measure obtained as the expectation of $\\pi_*\\mu$. We also prove that $\\pi_*\\mu$ is absolutely continuous with respect to $\\nu$ if and only if $\\dim(\\mu)>\\dim(\\nu)$, and find sufficient conditions for the equivalence of these measures. Our results provides a new proof of Dekking-Grimme"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09083","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"}