Simplices and Sets of Positive Upper Density in R
نویسندگان
چکیده
We prove an extension of Bourgain’s theorem on pinned distances in measurable subset of R2 of positive upper density, namely Theorem 1′ in [1], to pinned non-degenerate k-dimensional simplices in measurable subset of Rd of positive upper density whenever d ≥ k + 2 and k is any positive integer.
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تاریخ انتشار 2016