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We show that under some joint boundedness and twisted compactness conditions on the pairs $(A_i,T_i)$, almost everywhere convergence holds for all $f\\in L^2$. We also present resul"},"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":"1511.01528","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-04T22:00:37Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"27dfd7866698adcf67d19b7e24cd98b7fa008f2f83971b7c359c2a8e5a3c7aee","abstract_canon_sha256":"45e6ea1e9d580fd1bafc7416b631722025dd099208701a0b42a043000c66598f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:10.761129Z","signature_b64":"KjjdG+dBC6hUNExnLJZIoXInQAgtvFp/hUFzgMnqfrbm7m/sMKfFxT3SJvfXxLagN1bWkNQDs7XovMWrsORvDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e51d05f0ac3483f87ead49088627f9ddd971707a74948e8ad42a0f893947b9aa","last_reissued_at":"2026-05-18T01:03:10.760522Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:10.760522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Almost everywhere convergence of entangled ergodic averages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.DS","authors_text":"D\\'avid Kunszenti-Kov\\'acs","submitted_at":"2015-11-04T22:00:37Z","abstract_excerpt":"We study pointwise convergence of entangled averages of the form \\[ \\frac{1}{N^k}\\sum_{1\\leq n_1,\\ldots, n_k\\leq N} T_m^{n_{\\alpha(m)}}A_{m-1}T^{n_{\\alpha(m-1)}}_{m-1}\\ldots A_2T_2^{n_{\\alpha(2)}}A_1T_1^{n_{\\alpha(1)}} f, \\] where $f\\in L^2(X,\\mu)$, $\\alpha:\\left\\{1,\\ldots,m\\right\\}\\to\\left\\{1,\\ldots,k\\right\\}$, and the $T_i$ are ergodic measure preserving transformations on the standard probability space $(X,\\mu)$. We show that under some joint boundedness and twisted compactness conditions on the pairs $(A_i,T_i)$, almost everywhere convergence holds for all $f\\in L^2$. 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