{"paper":{"title":"Young's functional with Lebesgue-Stieltjes integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.CA","authors_text":"Dan Marinescu, Marian Stroe, Mihai Monea, Milan Merkle, Monica Moulin Ribeiro Merkle","submitted_at":"2011-10-07T21:13:24Z","abstract_excerpt":"For non-decreasing real functions $f$ and $g$, we consider the functional $ T(f,g ; I,J)=\\int_{I} f(x)\\di g(x) + \\int_J g(x)\\di f(x)$, where $I$ and $J$ are intervals with $J\\subseteq I$. In particular case with $I=[a,t]$, $J=[a,s]$, $s\\leq t$ and $g(x)=x$, this reduces to the expression in classical Young's inequality. We survey some properties of Lebesgue-Stieltjes interals and present a new simple proof for change of variables. Further, we formulate a version of Young's inequality with respect to arbitrary positive finite measure on real line including a purely discrete case, and discuss an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2950","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"}