INVESTIGADORES
MOLTER ursula Maria
artículos
Título:
On the Hausdorff h-measure of Cantor sets
Autor/es:
CABRELLI, CARLOS A.; MENDIVIL, FRANKLIN; MOLTER, URSULA M.; SHONKWILER, RONALD
Revista:
PACIFIC JOURNAL OF MATHEMATICS
Editorial:
Mathematical Science Publishers
Referencias:
Lugar: Berkeley, California; Año: 2004 vol. 217 p. 45 - 59
ISSN:
0030-8730
Resumen:
We estimate the Hausdorff measure and dimension of Cantor sets in terms of a sequence given by the lengths of the bounded complementary intervals. The results provide the relation between the decay rate of this sequence and the dimension of the associated Cantor set.  It is well known that not every Cantor set on the line is an $s$-set for some $0\leq s \leq 1$. However, if the sequence associated to the Cantor set $C$ is non-increasing, we show that $C$ is an $h$-set for some continuous, concave dimension function $h$. We construct the function $h$ from the sequence associated to the set $C$.