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On the Lp-improving property of the Cantor-Lebesgue measure Zhu, Junjie


The middle-third Cantor set is one of the most fundamental examples of self-similar fractal sets introduced by the German mathematician George Cantor in the late 1800s. Many questions about this set remain unanswered. In this thesis, we study the mapping property of a measure associated with the middle-third Cantor set. Specifically, we study whether the Cantor measure is Lebesgue improving through partly theoretical and partly numerical methods.

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