2017/11/17 by Han Yu, Yu, Han · 1 citation
Mathematics · Physics and Astronomy · #05B30 #28A78 #52C17 #Advanced Mathematical Theories and Applications #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical Dynamics and Fractals #math.CA #msc:05B30 #msc:28A78 #msc:52C17
paper · pdf · doi:10.48550/arxiv.1711.06533
The main content of this paper is covered in a new version of article 1711.06544. I want to merge article 1711.06533 and article 1711.06544 into the new version of article 1711.06544
openalex publication_date 2017/11/17 · arxiv created 2018/01/06 · arxiv updated 2018/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that in ℝn,n≥ 2, a compact set which contains n-1 spheres with all radii in [1/2,1] or with all possible centres in [0,1]n has full Hausdorff dimension. In fact the later set has positive Lebesgue measure. In this paper we consider a similar problem with sphere replacing by fractal cubes. The radii set and the centre set are also considered to be fractal sets. In addition we discuss the exceptional set in the setting of general largeness. In the end, an Furstenberg type example is discussed which can be somehow considered as the Furstenberg × 2, × 3 set conjecture (now theorem) in the setting of cubes/circles sets considered here.