{"paper":{"title":"Selections and their Absolutely Continuous Invariant Measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"A. Boyarsky, P. G\\'ora, Zh. Li","submitted_at":"2013-09-23T23:35:47Z","abstract_excerpt":"Let $I=[0,1]$ and consider disjoint closed regions $G_{1},....,G_{n}$ in $% I\\times I$ and subintervals $I_{1},......,I_{n},$ such that $G_{i}$ projects onto $I_{i.}$ We define the lower and upper maps $\\tau_{1},$ $\\tau_{2}$ by the lower and upper boundaries of $G_{i},i=1,....,n,$ respectively. We assume $\\tau_{1}$, $\\tau_{2}$ to be piecewise monotonic and preserving continuous invariant measures $\\mu_{1}$ and $\\mu_{2}$, respectively. Let $% F^{(1)}$ and $F^{(2)}$ be the distribution functions of $\\mu_{1}$ and $\\mu_{2}.$ The main results shows that for any convex combination $F$ of $% F^{(1)} "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6009","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"}