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Metric results on a new notion of discrepancy. (English) Zbl 0765.11031
By modifying a concept of I. M. Sobol’ and O. V. Nuzhdin [J. Number Theory 39, 367-373 (1991; Zbl 0743.11039)] the author obtains a new notion of discrepancy being more suitable for computational applications. He proves a law of the iterated logarithm and gives the connection to the usual discrepancy.

MSC:
11K38 Irregularities of distribution, discrepancy
60F15 Strong limit theorems
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References:
[1] FELLER W.: An Introduction to Probability Theory and Its Applications I, II. J. Wiley, New York, 1950. · Zbl 0039.13201
[2] HLAWKA E.: Theorie der Gleichverteilung. Bibliographisches Institut, Mannheim-Wien-Zurich, 1979. · Zbl 0406.10001
[3] KUIPERS L., NIEDERREITER H.: Uniform Distribution of Sequences. J. Wiley, New York, 1974. · Zbl 0281.10001
[4] PHILIPP W.: Mixing Sequences of Random Variables in Probabilistic Number Theory. AMS Memoirs vol. 114, Providence, 1971. · Zbl 0224.10052
[5] SOBOL I. M., NUSHDIN O. V.: A new measure of irregularity of distribution. J. Number Theory 39 (1991), 367-373. · Zbl 0743.11039
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