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摘要
For x is an element of (0,1), the univoque set for x, denoted u(x), is defined to be the set of beta is an element of(1,2) such that x has only one representation of the form x = x(1)/beta + x(2)/beta(2) +... with x(i) is an element of{0,1}. We prove that for any x is an element of(0, 1), u(x) contains a sequence {beta(k)}(k >= 1) increasing to 2. Moreover, u(x) is a Lebesgue null set of Hausdorff dimension 1; both u(x) and its closure <(u(x))over bar> are nowhere dense.
- 出版日期2014
- 单位华中科技大学
