{"paper":{"title":"Any law of group metric invariant is an inf-convolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mohammed Bachir","submitted_at":"2015-07-02T15:05:57Z","abstract_excerpt":"In this article, we bring a new light on the concept of the inf-convolution operation $\\oplus$ and provides additional informations to the work started in \\cite{Ba1} and \\cite{Ba2}. It is shown that any internal law of group metric invariant (even quasigroup) can be considered as an inf-convolution. Consequently, the operation of the inf-convolution of functions on a group metric invariant is in reality an extension of the internal law of $X$ to spaces of functions on $X$. We give an example of monoid $(S(X),\\oplus)$ for the inf-convolution structure, (which is dense in the set of all $1$-Lips"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00613","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"}