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BIRS Workshop Lecture Videos

Families of well-approximable measures Fairchild, Samantha


It is conjectured that the optimal order of approximation of the Lebesgue measure by a finite atomic measure is $N^{-1} (\log N)^{d-1}$. This result is known for dimensions 1 and 2. We will share recent work of Fairchild, Goering, Weiss which in dimension 1 confirms Lebesgue measure is indeed the hardest to approximate. Moreover we improve on recent work by Aistleitner, Bilyk, and Nikolov by constructing a family of discrete measures with star discrepancy bounded above by $N^{-1} (\log(N))$.

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