Poset limits can be totally ordered

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F15%3A00443353" target="_blank" >RIV/67985840:_____/15:00443353 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1090/S0002-9947-2015-06299-0" target="_blank" >http://dx.doi.org/10.1090/S0002-9947-2015-06299-0</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/S0002-9947-2015-06299-0" target="_blank" >10.1090/S0002-9947-2015-06299-0</a>

Result language
angličtina
Original language name
Poset limits can be totally ordered
Original language description
S. Janson [Poset limits and exchangeable random posets, Combinatorica 31 (2011), 529-563] defined limits of finite posets in parallel to the emerging theory of limits of dense graphs. We prove that each poset limit can be represented as a kernel on the unit interval with the standard order, thus answering an open question of Janson. We provide two proofs: real-analytic and combinatorial. The combinatorial proof is based on a Szemerédi-type Regularity Lemma for posets which may be of independent interest. Also, as a by-product of the analytic proof, we show that every atomless ordered probability space admits a measure-preserving and almost order-preserving map to the unit interval.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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