{"paper":{"title":"The existence of sigma-finite invariant measures, applications to real one-dimensional dynamics","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Marco Martens","submitted_at":"1992-01-15T00:00:00Z","abstract_excerpt":"A general construction for $\\sigma-$finite absolutely continuous invariant measure will be presented. It will be shown that the local bounded distortion of the Radon-Nykodym derivatives of $f^n_*(\\lambda)$ will imply the existence of a $\\sigma-$finite invariant measure for the map $f$ which is absolutely continuous with respect to $\\lambda$, a measure on the phase space describing the sets of measure zero. Furthermore we will discuss sufficient conditions for the existence of $\\sigma-$finite invariant absolutely continuous measures for real 1-dimensional dynamical systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9201300","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"}