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We also show that $BV_{\\frac{n}{n-1}}(\\mathbb{R}^n)^*$ and $BV(\\mathbb{R}^n)^*$ are isometrically isomorphic, where $BV(\\mathbb{R}^n)$ is defined as the space of all functions $u$ in $L^{1}(\\mathbb{R}^n)$ such that $Du$ is a finite vector-valued measure. As a consequence of our characterizations, an old issue raised in Meyers-Ziemer [MZ] is resol"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1503.06208","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-20T19:54:26Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"c73904b90da68b8ca604248a913639ba09ff48a01956d7b57c3fbdf618faaeba","abstract_canon_sha256":"64ac3fff3c97f8836081f26df92ab6917fff0c662c6d3ae3bd14c3ba6beb2630"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:48.283400Z","signature_b64":"kbidEVt5BHM6amGbpVzqKadU8if4/hHfdaKQOPQ/YisQFG40ZbSOObqljWtiAuaXtXj4Ds8vV7dYGOUdqy5PDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c9152839ca0dc9248aa5888b3ce3a60327914d0e9cc88445fcaab26516210fb","last_reissued_at":"2026-05-18T02:20:48.282550Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:48.282550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterizations of signed measures in the dual of $BV$ and related isometric isomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Monica Torres, Nguyen Cong Phuc","submitted_at":"2015-03-20T19:54:26Z","abstract_excerpt":"We characterize all (signed) measures in $BV_{\\frac{n}{n-1}}(\\mathbb{R}^n)^*$, where $BV_{\\frac{n}{n-1}}(\\mathbb{R}^n)$ is defined as the space of all functions $u$ in $L^{\\frac{n}{n-1}}(\\mathbb{R}^n)$ such that $Du$ is a finite vector-valued measure. 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