{"paper":{"title":"Pointwise Convergence of Ergodic Averages Along Integer Cantor Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.PR"],"primary_cat":"math.DS","authors_text":"Alex Iosevich, Ben Krause, F\\'elix Brokering Pinilla","submitted_at":"2026-07-17T15:44:52Z","abstract_excerpt":"Let $d \\geq 3$,\n  \\[ D \\subsetneq \\{ 0,1,\\dots,d-1\\}, \\qquad |D| \\geq 2, \\ 0 \\in D \\]\n  be a finite alphabet, and define the integer Cantor set\n  \\begin{align} \\mathcal{C} := \\mathcal{C}_{D} := \\bigcup_{J \\geq 0} \\Big\\{ \\sum_{j =0}^J a_j d^j : a_j \\in D \\Big\\}.\n  \\end{align} We prove that for any $\\sigma$-finite measure-preserving system, $(X,\\mu,T)$, and any $f \\in L^p(X)$, $2\\leq p<\\infty$, the ergodic averages \\begin{align}\n  \\frac{1}{|\\mathcal{C}_N|} \\sum_{n \\in \\mathcal{C}_N } f(T^n x), \\qquad \\mathcal{C}_N := \\mathcal{C} \\cap \\{1,2,\\dots,N \\} \\end{align}\n  converge $\\mu$-almost everywher"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16064","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.16064/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}