{
  "abstract": "We study entropy realization for continuous actions of infinite countable amenable groups. We introduce an approximate product property for amenable group actions that permits a small proportion of tracing mistakes on prescribed pairwise disjoint, sufficiently invariant finite sets. We prove that this property implies entropy-denseness and almost entropy-approximability of every invariant measure. The construction combines zero-entropy exact tilings with a finite-block estimate for the complexity of tracing mistakes. Under asymptotic entropy expansiveness, almost entropy-approximability upgrades to entropy-approximability. For every $0\\leqα<h(X,G)$, ergodic measures of entropy $α$ then form a residual subset of the invariant measures whose entropy is at least $α$. In particular, the set of ergodic measure entropies equals $[0,h(X,G)]$.37A35, 37B40, 37B05",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09949",
  "author_total": 2,
  "authors": [
    {
      "name": "Wenda Zhang"
    },
    {
      "name": "Xiankun Ren"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/73q3xqwh0d94x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09949",
  "fulltext_url": null,
  "id": "73q3xqwh0d94x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09949",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7220934550",
  "pdf_url": "https://arxiv.org/pdf/2610.09949",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/73q3xqwh0d94x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09949",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09949"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Ergodic measures of intermediate entropies for amenable group actions with an approximate product property",
  "title_text": "Ergodic measures of intermediate entropies for amenable group actions with an approximate product property",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/73q3xqwh0d94x",
  "venue": "arXiv",
  "versions": []
}