On the parametrization of self-similar and other fractal sets

摘要

We prove for many self-similar, and some more general, sets E subset of R-n that if s is the Hausdorff dimension of E and f : R-m --> R-n is Holder continuous with exponent m/s, then the s-dimensional Hausdorff measure of E boolean AND f(R-m) is 0. [References: 8]