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Correcting continuous hypergraphs


Author: F. Petrov
Translated by: F. Petrov
Original publication: Algebra i Analiz, tom 28 (2016), nomer 6.
Journal: St. Petersburg Math. J. 28 (2017), 783-787
MSC (2010): Primary 05C65
DOI: https://doi.org/10.1090/spmj/1473
Published electronically: October 2, 2017
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Abstract: A general result in the spirit of the continuous hypergraph removal lemma is stated and proved: if a ``closed'' property of values of a measurable function on $ [0,1]^n$ holds almost everywhere, then the function may be changed on a set of measure 0 so that this property holds everywhere. It is also shown that in some situations a discrete version fails.


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Additional Information

F. Petrov
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, 191023 St. Petersburg, Russia
Email: fedyapetrov@gmail.com

DOI: https://doi.org/10.1090/spmj/1473
Keywords: Removal lemma, continuous hypergraph, Ramsey theorem
Received by editor(s): July 19, 2016
Published electronically: October 2, 2017
Additional Notes: Supported by St. Petersburg State University grants nos. 6.38.223.2014 and 6.37.208.2016 and by RFBR grant no. 14-01-00373a.
Article copyright: © Copyright 2017 American Mathematical Society