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SUMMARY:A measurable version of the Lovász Local Lemma - Gábor Kun (ELTE
 \, Budapest)
DTSTART:20130124T143000Z
DTEND:20130124T153000Z
UID:TALK42921@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:I shall prove a measurable version of the LLL that will allow 
 to prove theorems of the following kind.\n\nLet $G$ be a compact group wit
 h a Borel probability\nmeasure\, and let $S_1\, \\dots \, S_n$ be $k$-elem
 ent subsets of $G$\, where $\\frac{2 e n k^2}{2^k} < 1$ and $\\varepsilon 
 > 0$. Then there are measurable subsets $A$ and $B$ of $G$ such that their
  intersection has measure less than $\\varepsilon$\, and every shift $gS_i
 $ of one of the sets intersects both $A$ and $B$.\n\nThe measurable LLL re
 quires the same local conditions as the discrete LLL: it gives a measurabl
 e colouring (evaluation)\, but an unfortunate error of measure $\\varepsil
 on$ might occur. I shall apply this measurable LLL to give another solutio
 n to the dynamical von Neumann problem of Gaboriau and Lyons. This proof i
 s based on the ideas of the proof of the algorithmic LLL due to Moser and 
 Tardos.
LOCATION:MR12
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