Currently displaying 1 – 1 of 1

Showing per page

Order by Relevance | Title | Year of publication

Besicovitch subsets of self-similar sets

Ji-Hua MaZhi-Ying WenJun Wu — 2002

Annales de l’institut Fourier

Let E be a self-similar set with similarities ratio r j ( 0 j m - 1 ) and Hausdorff dimension s , let p ( p 0 , p 1 ) ... p m - 1 be a probability vector. The Besicovitch-type subset of E is defined as E ( p ) = x E : lim n 1 n k = 1 n χ j ( x k ) = p j , 0 j m - 1 , where χ j is the indicator function of the set { j } . Let α = dim H ( E ( p ) ) = dim P ( E ( p ) ) = j = 0 m - 1 p j log p j j = 0 m - 1 p i log r j and g be a gauge function, then we prove in this paper:(i) If p = ( r 0 s , r 1 s , , r m - 1 s ) , then s ( E ( p ) ) = s ( E ) , 𝒫 s ( E ( p ) ) = 𝒫 s ( E ) , moreover both of s ( E ) and 𝒫 s ( E ) are finite positive;(ii) If p is a positive probability vector other than ( r 0 s , r 1 s , , r m - 1 s ) , then the gauge functions can be partitioned as follows ...

Page 1

Download Results (CSV)