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A note on antichains in the continuous cube
Published 8 Nov 2019 in math.CO and math.MG | (1911.03421v1)
Abstract: It is well-known that an antichain in the poset $[0,1]n$ must have measure zero. Engel, Mitsis, Pelekis and Reiher showed that in fact it must have $(n-1)$-dimensional Hausdorff measure at most $n$, and they conjectured that this bound can be attained. In this note we show that, for every $n$, such an antichain does indeed exist.
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