{"paper":{"title":"Pointwise Equidistribution and Translates of Measures on Homogeneous Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Osama Khalil","submitted_at":"2017-03-21T13:57:07Z","abstract_excerpt":"Let $(X,\\mathfrak{B},\\mu)$ be a Borel probability space. Let $T_n: X\\rightarrow X$ be a sequence of continuous transformations on $X$. Let $\\nu$ be a probability measure on $X$ such that $\\frac{1}{N}\\sum_{n=1}^N (T_n)_\\ast \\nu \\rightarrow \\mu$ in the weak-$\\ast$ topology. Under general conditions, we show that for $\\nu$ almost every $x\\in X$, the measures $\\frac{1}{N}\\sum_{n=1}^N \\delta_{T_n x}$ get equidistributed towards $\\mu$ if $N$ is restricted to a set of full upper density. We present applications of these results to translates of closed orbits of Lie groups on homogeneous spaces. As a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07224","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"}