Metric Diophantine Approximation on Manifolds

By V. Bernik, M. Dodson. 2000

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Hausdorff measure of sets of Dirichlet non-improvable numbers (2017, background): “For further details we refer to the beautiful texts [3, 5].”
Measure Theoretic Laws for Lim Sup Sets (2004, background): “am(r) ≤ m(B(x,r)) ≤ bm(r) 1The statement of the Theorem 1 in [18] is not correct when δ= γand the proof assumes that limr→∞ ψ(r) = 0. Also, a weaker statement of Corollary 6 appears as Theorem 5.6 in [10]. However, the proof contains a ﬂaw. The claim that a certain set T∞ is a subset of Λ(ψ) is not ”
Mass transference principle from rectangles to rectangles in Diophantine approximation (2019, background): “Both of them perform sufficiently well in catching the essential nature for the dimensional theory of limsup set for balls (see [5], [6], [12], [15], [35], [42], etc for applications).”