Measurable Sets With Excluded Distances
نویسندگان
چکیده
منابع مشابه
Measurable sets with excluded distances
For a set of distances D = {d1, . . . , dk} a set A is called D-avoiding if no pair of points of A is at distance di for some i. We show that the density of A is exponentially small in k provided the ratios d1/d2, d2/d3, . . . , dk−1/dk are all small enough. This resolves a question of Székely, and generalizes a theorem of Furstenberg-Katznelson-Weiss, Falconer-Marstrand, and Bourgain. Several ...
متن کاملList colorings with measurable sets
The measurable list chromatic number of a graph G is the smallest number ξ such that if each vertex v of G is assigned a set L(v) of measure ξ in a fixed atomless measure space, then there exist sets c(v) ⊆ L(v) such that each c(v) has measure one and c(v) ∩ c(v′) = ∅ for every pair of adjacent vertices v and v′. We provide a simpler proof of a measurable generalization of Hall’s theorem due to...
متن کاملMeasure zero sets with non - measurable sum
For any C ⊆ R there is a subset A ⊆ C such that A + A has inner measure zero and outer measure the same as C + C. Also, there is a subset A of the Cantor middle third set such that A+A is Bernstein in [0, 2]. On the other hand there is a perfect set C such that C + C is an interval I and there is no subset A ⊆ C with A + A Bernstein in I.
متن کاملEffectively approximating measurable sets by open sets
We answer a recent question of Bienvenu, Muchnik, Shen, and Vereshchagin. In particular, we prove an effective version of the standard fact from analysis which says that, for any ε > 0 and any Lebesgue-measurable subset of Cantor space, X ⊆ 2, there is an open set Uε ⊆ 2, Uε ⊇ X, such that μ(Uε) ≤ μ(X) + ε, where μ(Z) denotes the Lebesgue measure of Z ⊆ 2. More specifically, our main result sho...
متن کاملNull-Control and Measurable Sets
We prove the interior and boundary null–controllability of some parabolic evolutions with controls acting over measurable sets.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Geometric and Functional Analysis
سال: 2008
ISSN: 1016-443X,1420-8970
DOI: 10.1007/s00039-008-0673-8