Irregularities of distribution for bounded sets and half‐spaces

@article{Brandolini2022IrregularitiesOD,
  title={Irregularities of distribution for bounded sets and half‐spaces},
  author={Luca Brandolini and Leonardo Colzani and Giancarlo Travaglini},
  journal={Mathematika},
  year={2022},
  volume={69}
}
We prove a general result on irregularities of distribution for Borel sets intersected with bounded measurable sets or affine half‐spaces. 

References

SHOWING 1-10 OF 32 REFERENCES

Diameter Bounded Equal Measure Partitions of Ahlfors Regular Metric Measure Spaces

The algorithm devised by Feige and Schechtman for partitioning higher dimensional spheres into regions of equal measure and small diameter is combined with David’s and Christ’s constructions of

Ten lectures on the interface between analytic number theory and harmonic analysis

Uniform distribution van der Corput sets Exponential sums I: The methods of Weyl and van der Corput Exponential sums II: Vinogradov's method An introduction to Turan's method Irregularities of

Discrepancy of point sequences on fractal sets

We consider asymptotic bounds for the discrepancy of point sets on a class of fractal sets. By a method of R. Alexander, we prove that for a wide class of fractals, the L2-discrepancy (and

Discrepancy and Numerical Integration on Metric Measure Spaces

We study here the error of numerical integration on metric measure spaces adapted to a decomposition of the space into disjoint subsets. We consider both the error for a single given function, and

Techniques in fractal geometry

Mathematical Background. Review of Fractal Geometry. Some Techniques for Studying Dimension. Cookie-cutters and Bounded Distortion. The Thermodynamic Formalism. The Ergodic Theorem and Fractals. The

The discrepancy method - randomness and complexity

This book tells the story of the discrepancy method in a few short independent vignettes. It is a varied tale which includes such topics as communication complexity, pseudo-randomness, rapidly mixing

Irregularities of Distribution and Average Decay of Fourier Transforms

In Geometric Discrepancy we usually test a distribution of N points against a suitable family of sets. If this family consists of dilated, translated and rotated copies of a given d-dimensional

Fourier Analysis and Hausdorff Dimension

Preface Acknowledgements 1. Introduction 2. Measure theoretic preliminaries 3. Fourier transforms 4. Hausdorff dimension of projections and distance sets 5. Exceptional projections and Sobolev

An elementary approach to lower bounds in geometric discrepancy

A proof of the lower bound is presented, which is based on Alexander's technique but is technically simpler and more accessible, and three variants of the proof are presented to provide more intuitive insight into the “large-discrepancy” phenomenon.

On irregularities of distribution.

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