On the Hausdorff dimension of some graphs

  title={On the Hausdorff dimension of some graphs},
  author={R. Daniel Mauldin and S. C. Williams},
  journal={Transactions of the American Mathematical Society},
Consider the functions Wb(x)= b-cn[1(bnX + On)--1(0n)] n=-oo where b > 1, 0 0 such that if b is large enough, then the Hausdorff dimension of the graph of Wb is bounded below by 2a (C/ ln b). We also show that if a function f is convex Lipschitz of order a, then the graph of f has a-finite measure with respect to Hausdorff's measure in dimension 2 a. The convex Lipschitz functions of order a include Zygmund's class A,. Our analysis shows that the graph of the classical van der WaerdenTagaki… 
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