A FUNCTION WHOSE GRAPH HAS POSITIVE DOUBLING MEASURE

作者：Ojala Tuomo^*; Rajala Tapio

来源：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 144(2): 733-738.

DOI：10.1090/proc12748

• Doubling measure
• thin set
• fat set

We show that a doubling measure on the plane can give positive measure to the graph of a continuous function. This answers a question by Wang, Wen and Wen posed in a 2013 paper. Moreover, we show that the doubling constant of the measure can be chosen to be arbitrarily close to the doubling constant of the Lebesgue measure.

• 出版日期2016-2