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Exceptional Sets in Uniform Distribution

Published online by Cambridge University Press:  20 January 2009

R. C. Baker
R. C. Baker
Affiliation:
Royal Holloway College, Egham, Surrey
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Let B be a measurable set of real numbers in (0,1) of Lebesgue measure |B| and let x1, …, xn be real. Then

denotes the number of j (1 ≦j≦n) for which the fractional part {xj}∈B. The discrepancy of x1, …, xn is

where the supremum is taken over all intervals I in [0,1].

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 22 , Issue 2 , June 1979 , pp. 145 - 160
Copyright
Copyright © Edinburgh Mathematical Society 1979

References

REFERENCES

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