INVESTIGADORES
PANZONE Pablo Andres
artículos
Título:
Some comments on the Hausdorff measure of self-similar sets
Autor/es:
PANZONE PABLO A.
Revista:
Volumena de homenaje a R. Ricabarra
Editorial:
X
Referencias:
Lugar: Bahia Blanca; Año: 1995 p. 35 - 52
ISSN:
0328-2600
Resumen:
he Hausdorff dimension of a self-similar set $E$E is a local property of the set. Its Hausdorff measure $H^S(E)$HS(E) can be determined by looking at the construction process in an arbitrarily small neighborhood of any of its points. Methods of calculating $H^S(E)$HS(E) or lower bounds for it are given and discussed. They are applied to the Sierpiński gasket, obtaining upper and lower bounds for its Hausdorff measure. It is proved that a limit process is unavoidable if one wishes to calculate precisely the measure of this fractal set.