Bi-Lipschitz mappings and quasinearly subharmonic functions.
Two ideals connected with strong right upper porosity at a point
Let be the set of upper strongly porous at subsets of and let be the intersection of maximal ideals . Some characteristic properties of sets are obtained. We also find a characteristic property of the intersection of all maximal ideals contained in a given set which is closed under subsets. It is shown that the ideal generated by the so-called completely strongly porous at subsets of is a proper subideal of Earlier, completely strongly porous sets and some of their properties were...
Linear distortion of Hausdorff dimension and Cantor's function.
Let be a mapping from a metric space X to a metric space Y, and let α be a positive real number. Write dim (E) and H(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)) = αdim (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 H(M) = 1, with s = log2/log3 and dim(G(E)) = (log3/log2) dim (E), for every...
Page 1