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math.CA2020
Dimension of Images of Large Level Sets
Anthony G. O'Farrell, Gavin Armstrong
Let be a natural number. We consider -times continuously-differentiable real-valued functions , where is some interval on the line having positive leng…
math.CA2016
A pathological construction for real functions with large collections of level sets
Gavin Armstrong
Consider all the level sets of a real function. We can group these level sets according to their Hausdorff dimensions. We show that the Hausdorff dimension of the collection of all…