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Uniform Distribution in Model Sets
Canadian Mathematical Bulletin, 2002AbstractWe give a new measure-theoretical proof of the uniform distribution property of points in model sets (cut and project sets). Each model set comes as a member of a family of related model sets, obtained by joint translation in its ambient (the ‘physical’) space and its internal space. We prove, assuming only that the window defining themodel set
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A theorem on uniform distribution
1963Es sei \(\{I_j\}^\infty_{j=1}\) eine Folge von paarweise elementfremden Intervallen \(I_j = (x_j,y_j)\) derart, daß \(0 \leq x_1 < y_1 < x_2 < y_2 < \cdots\) und \(\lim_{j \to \infty} x_j = \infty\) gilt. Für \(Z>0\) sei \(I(Z)\) das Lebesguesche Maß der Punktmenge \(\cup_{j=1}^{\infty} I_j \cap (0,Z)\). Für \(\alpha > 0\) und für jede natürliche Zahl \
Davenport, H., Erdős, P.
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