Small Furstenberg sets
نویسندگان
چکیده
منابع مشابه
Furstenberg Sets for a Fractal Set of Directions
In this paper we study the behavior of the size of Furstenberg sets with respect to the size of the set of directions defining it. For any pair α, β ∈ (0, 1], we will say that a set E ⊂ R2 is an Fαβ-set if there is a subset L of the unit circle of Hausdorff dimension at least β and, for each direction e in L, there is a line segment e in the direction of e such that the Hausdorff dimension of t...
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A set A ⊆ N is called complete if every sufficiently large integer can be written as the sum of distinct elements of A. In this paper we present a new method for proving the completeness of a set, improving results of Cassels (’60), Zannier (’92), Burr, Erdős, Graham, and Li (’96), and Hegyvári (’00). We also introduce the somewhat philosophically related notion of a dispersing set and refine a...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2013
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2012.11.001