Abstract
In the paper ‘Discrepancy and distance between sets’ G. Myerson studied several notions of distances and discrepancies of point distributions on the unit interval. Among several results he proves an inequality between p-discrepancy ( p ≥ 1) and the ‘distance’ between n-element subsets of the unit interval. This paper contains a proof of his conjecture that this inequality holds in a stronger version. Furthermore it can be transferred to arbitrary probability distributions on the unit interval which are Borel measures. The results can be embedded into a topological context. The last section contains a corollary which is a further expansion of the inequality's domain of validity.
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