Hausdorff dimension and approximation of smooth functions.
نویسندگان
چکیده
منابع مشابه
Hausdorff dimension and Diophantine approximation
In the present survey paper, we explain how the theory of Hausdorff dimension and Hausdorff measure is used to answer certain questions in Diophantine approximation. The final section is devoted to a discussion around the Diophantine properties of the points lying in the middle third Cantor set.
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A general form of the Borel-Cantelli Lemma and its connection with the proof of Khintchine's Theorem on Diophantine approximation and the more general Khintchine-Groshev theorem are discussed. The torus geometry in the planar case allows a relatively direct proof of the planar Groshev theorem for the set of ψ-approximable points in the plane. The construction and use of Haudsorff measure and di...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1973
ISSN: 0026-2285
DOI: 10.1307/mmj/1029001012