{"paper":{"title":"Integration and measures on the space of countable labelled graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.CA","authors_text":"Apoorva Khare, Bala Rajaratnam","submitted_at":"2015-06-04T00:39:42Z","abstract_excerpt":"In this paper we develop a rigorous foundation for the study of integration and measures on the space $\\mathscr{G}(V)$ of all graphs defined on a countable labelled vertex set $V$. We first study several interrelated $\\sigma$-algebras and a large family of probability measures on graph space. We then focus on a \"dyadic\" Hamming distance function $\\left\\| \\cdot \\right\\|_{\\psi,2}$, which was very useful in the study of differentiation on $\\mathscr{G}(V)$. The function $\\left\\| \\cdot \\right\\|_{\\psi,2}$ is shown to be a Haar measure-preserving bijection from the subset of infinite graphs to the ci"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01439","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"}