Publication: Dependent measures in independent theories
| dc.contributor.author | Khanaki, Karim | |
| dc.date.accessioned | 2025-07-23T21:24:38Z | |
| dc.date.issued | 2026 | |
| dc.description.abstract | We introduce the notion of <em>dependence</em>, as a property of a Keisler measure, and generalize some results of Hrushovski, Pillay & Simon (2013) in NIP theories (theories satisfying the negation of the independence property) to arbitrary theories. Among other things, we show that this notion is very natural and fundamental for several reasons: <ol> <li>all measures in NIP theories are dependent,</li> <li>all types and all frequency interpretation measures (fims) in any theory are dependent, and</li> <li>as a crucial result in measure theory, the Glivenko–Cantelli class of functions (formulas) is characterized by dependent measures.</li> </ol> | |
| dc.identifier.citation | Karim Khanaki. "Dependent measures in independent theories." Zeitschrift für Mathematische Logik und Grundlagen der Mathematik: to appear (2026). DOI: 10.60866/CAM.253. | |
| dc.identifier.uri | https://diamond-oa.lib.cam.ac.uk/handle/1812/445 | |
| dc.identifier.uri | https://doi.org/10.60866/CAM.253 | |
| dc.rights | Attribution 4.0 International | en |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | |
| dc.title | Dependent measures in independent theories | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 25499239-ccc3-4ef1-8033-15fa55080c1f | |
| relation.isAuthorOfPublication.latestForDiscovery | 25499239-ccc3-4ef1-8033-15fa55080c1f | |
| relation.isJournalOfPublication | 72325bdb-b61c-4cc3-a98c-4e01c7b9a035 | |
| relation.isJournalVolumeOfPublication | 411f67b4-727b-42d6-af85-424be70ea060 | |
| relation.isJournalVolumeOfPublication.latestForDiscovery | 411f67b4-727b-42d6-af85-424be70ea060 |