[Settfa] Tuesday 05/11, Christos Pelekis

[kubis at math.cas.cz]

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 Tuesday 5th November, 10:00am 
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 Speaker:Christos Pelekis, IM CAS
 Title: A continuous analogue of Erdös' k-Sperner theorem

 Abstract  

 A chain in the unit n-cube is a set C having the property that for any two points in C, one is coordinate-wise dominating the other. I will show that the 1-dimensional Hausdorff measure of a chain in the unit n-cube is at most n, and that the bound is sharp. Moreover, I will discuss the problem of maximising the n-dimensional Lebesgue measure of a measurable subset, A, of the unit n-cube, subject to the constraint that the 1-dimensional Hausdorff measure of its intersection with every chain is at most \kappa, where \kappa is a fixed real number from the interval (0,n]. Our main result provides a sharp upper bound on the n-dimensional Lebesgue measure of A and may be seen as a continuous analogue of Erdös' theorem on k-Sperner families of finite sets. This is joint work with Themis Mitsis and Václav Vlasák.

 For more information see the seminar web page at 
 https://calendar.math.cas.cz/set-theory-and-analysis-actual .