DOUBLING MEASURES WITH DOUBLING CONTINUOUS PART

作者：Lou Man Li^*; Wu Min

来源：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 138(10): 3585-3589.

DOI：10.1090/S0002-9939-10-10358-X

• doubling measure
• purely atomic
• continuous part

We prove that every compact subset of R(d) of positive Lebesgue measure carries a doubling measure which is not purely atomic. Also, we prove that for every compact and nowhere dense subset E of R(d) without isolated points and for every doubling measure mu on E there is a countable set F with E boolean AND F = empty set and a doubling measure nu on E boolean OR F such that nu vertical bar(E) = mu. This shows that there are many doubling measures whose continuous part is doubling.

• 出版日期2010-10
• 单位华南理工大学