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math.CA2014
A function whose graph has positive doubling measure
Tuomo Ojala, Tapio Rajala
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 th…
math.MG2014
Failure of topological rigidity results for the measure contraction property
Christian Ketterer, Tapio Rajala
We give two examples of metric measure spaces satisfying the measure contraction property MCP(K,N) but having different topological dimensions at different regions of the space. Th…