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Under the same hypothesis we prove that for any action $a$ of $G$, if $b$ is a free action of $G/H$, and $b_G$ is the induced action of $G$ then $\\CInd_H^G(a|H) \\times b_G$ weakly contains $a$. Moreover, if $H<G$ is any subgroup of a countable group $G$, and the action of $G$ on $G/H$ is amenable, then $\\CInd_H^G(a|H)$ weakly contains $a$ whenever $a$ is a Gaussian action."},"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":"1105.0648","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-05-03T18:25:38Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"608447c505c223c36e24ee4551614ee58d0dd49a90d3b76e12bffeb0969fe624","abstract_canon_sha256":"980678e517295dbd304e9886f808645fd4045a054bad22c58a37525fbe136790"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:30.642266Z","signature_b64":"ZqYOlX4EG2F6k/9jWC2ff4z5xQVkGZLJY0dH1GQ2uL5SRpx29PgEEllBL6Y7eT7GwIW8dxE8uz65aKB2CDMqDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67573e5fd2678c0e80bc2d5e9b602f3f26feb4ca3bb46873f8e1a1338d7e4c28","last_reissued_at":"2026-05-18T04:16:30.641878Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:30.641878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a co-induction question of Kechris","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GR","authors_text":"Lewis Bowen, Robin Tucker-Drob","submitted_at":"2011-05-03T18:25:38Z","abstract_excerpt":"This note answers a question of Kechris: if $H<G$ is a normal subgroup of a countable group $G$, $H$ has property MD and $G/H$ is amenable and residually finite then $G$ also has property MD. Under the same hypothesis we prove that for any action $a$ of $G$, if $b$ is a free action of $G/H$, and $b_G$ is the induced action of $G$ then $\\CInd_H^G(a|H) \\times b_G$ weakly contains $a$. 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