Journals / Turkish Journal of Mathematics / 2001 / Cilt: 25 - Sayı: 4

On the Lebesgue Measure of Self-Affine Sets

Pages
535–543
Publication Date
2022-11-03
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The attractors we obtain include the Haar-type multi-tiles of Flaherty and Wang.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Flaherty and Wang studied Haar-type multiwavelets and multi-tiles.
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Key Findings & Data:The information on what digit sets give multi-attractors with positive Lebesgue measure is very limited.
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Conclusion & Impact:The attractors we obtain include the Haar-type multi-tiles of Flaherty and Wang.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Multi-attractors · self-affine tiles · iterated function systems.

Abstract

Flaherty and Wang studied Haar-type multiwavelets and multi-tiles. The information on what digit sets give multi-attractors with positive Lebesgue measure is very limited. In this note, we give a few classes of digit sets leading to multi-attractors with positive measure. The attractors we obtain include the Haar-type multi-tiles of Flaherty and Wang.

Özet

Flaherty and Wang studied Haar-type multiwavelets and multi-tiles. The information on what digit sets give multi-attractors with positive Lebesgue measure is very limited. In this note, we give a few classes of digit sets leading to multi-attractors with positive measure. The attractors we obtain include the Haar-type multi-tiles of Flaherty and Wang.

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Cite This Article

KIRAT, İ. (2022). On the Lebesgue Measure of Self-Affine Sets. Turkish Journal of Mathematics, Cilt: 25 - Sayı: 4, 535–543. https://ajindex.com/articles/608907

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