Search results for "fat set"

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A function whose graph has positive doubling measure

2014

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.

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::DatabasesMathematicsProceedings of the American Mathematical Society
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