# Inverting the Furstenberg correspondence

@inproceedings{Avigad2011InvertingTF, title={Inverting the Furstenberg correspondence}, author={Jeremy Avigad}, year={2011} }

Given a sequence of subsets A_n of {0,...,n-1}, the Furstenberg correspondence principle provides a shift-invariant measure on Cantor space that encodes combinatorial information about infinitely many of the A_n's. Here it is shown that this process can be inverted, so that for any such measure there are finite sets whose combinatorial properties approximate it arbitarily well. Moreover, we obtain an explicit upper bound on how large n has to be to obtain a sufficiently good approximation. As a… CONTINUE READING

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