6533b833fe1ef96bd129c1c3
RESEARCH PRODUCT
A function whose graph has positive doubling measure
Tuomo OjalaTapio Rajalasubject
Discrete mathematics28A12 (Primary) 30L10 (Secondary)Lebesgue measureApplied MathematicsGeneral Mathematicsta111thin setThin setMathematics - Classical Analysis and ODEsfat setdoubling measureClassical Analysis and ODEs (math.CA)FOS: MathematicsGraph (abstract data type)Computer Science::DatabasesMathematicsdescription
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. 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-06-18 | Proceedings of the American Mathematical Society |