Measures with specified support and arbitrary Assouad dimensions

We show that if the upper Assouad dimension of the compact set E ⊆ R is positive, then given any D > dimA E there is a measure with support E and upper Assouad (or regularity) dimension D. Similarly, given any 0 ≤ d < dimL E, there is a measure on E with lower Assouad dimension d.Fil: Hare, Kathryn E.. University of Waterloo; CanadáFil: Mendivil, Franklin. Acadia University; CanadáFil: Zuberman, Leandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina. Universidad Nacional de Mar del Plata. Facultad de Cs.exactas y Naturales. Centro Marplatense de Investigaciones Matematicas.; Argentin