Resumen de Linear distortion of Hausdorff dimension and Cantor's function

Matti Vuorinen, V. Ryazanov

• Let f be a mapping from a metric space X to a metric space Y , and let ! be a positive real number. Write dim(E) and Hs(E) for the Hausdorff dimension and the s-dimensional Hausdorff measure of a set E. We give sufficient conditions that the equality dim(f(E)) = ! dim(E) holds for each E " X. The problem is studied also for the Cantor ternary function G. It is shown that there is a subset M of the Cantor ternary set such that Hs(M) = 1, with s = log 2/log 3 and dim(G(E)) = (log 3/log 2) dim(E), for every E " M.