Boca 2008 problem erdos szusz turan diophantine approximations

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Florin P. Boca, A problem of Erdős, Szüsz and Turán concerning Diophantine approximations, International Journal of Number Theory 4 (2008), no. 4, 691–708. DOI:10.1142/S1793042108001626.

The abstract says the paper proves directly that the Lebesgue measure of $S(N,A,c)$ (there the set itself; Problem 1001's $S(N,A,c)$ is its measure) has a limit $f(A,c)$ as $N\to\infty$, and identifies that limit for all $A>0$ and $c>1$. By the abstract, this completes the evaluation asked for in Problem 1001, beyond the existence result of Kesten and Sós and Kesten's explicit computation for $Ac\le1$. This card records DOI metadata and the abstract; the full paper has not been read here.

Bears on. Problem 1001: explicit limit.