Cassels 1950 some metrical theorems diophantine approximation i

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J. W. S. Cassels, Some metrical theorems in Diophantine approximation. I, Proceedings of the Cambridge Philosophical Society 46 (1950), 209–218. DOI:10.1017/S0305004100025676.

The maintained entry for Problem 1000 cites Cassels for introducing the quantity $\phi_A$ and obtaining a sequence with zero lower limit of the associated averages. The problem asks for a full limit of zero, which the entry attributes to Haight. This card records DOI metadata; the Cassels paper has not been read here.

Bears on. Problem 1000: liminf precursor.