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On a characterisation of Dirac measures

Published online by Cambridge University Press:  14 November 2011

Miguel Escobedo
Miguel Escobedo
Affiliation:
Laboratoire d'Analyse Numerique, Université Pierre et Marie Curie, Tour 55-65 - 5ème étage, 4, place Jussieu, 75230 Paris Cedex 05, France
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Synopsis

Assume f ∈ C(RM, SN−1) (M ≧ 1, N ≧ 1) is periodic with period one in each variable and satisfies:

Then, every probability measure on [0, 1)M such that

is a Dirac measure at some point of [0, 1)M.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 103 , Issue 3-4 , 1986 , pp. 253 - 264
Copyright
Copyright © Royal Society of Edinburgh 1986

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References

1Kuipers, L. and Niederreiter, H.. Uniform Distribution of Sequences (New York: John Wiley & Sons, 1974).Google Scholar