In this paper the problem of determining if a given measure is irrigable, in the sense of [4], or not is addressed. A notion of irrigability dimension of a measure is given and lower and upper bounds are proved in terms of the minimal Hausdorff and respectively Minkowski dimension of a set on which the measure is concentrated. A notion of resolution dimension of a measure based on its discrete approximations is also introduced and its relation with the irrigation dimension is studied
On the dimension of an irrigable measure / Devillanova, Giuseppe; Solimini, Sergio Fausto. - In: RENDICONTI DEL SEMINARIO MATEMATICO DELL'UNIVERSITA' DI PADOVA. - ISSN 0041-8994. - 117:(2007), pp. 1-49.
On the dimension of an irrigable measure
DEVILLANOVA, Giuseppe;SOLIMINI, Sergio Fausto
2007-01-01
Abstract
In this paper the problem of determining if a given measure is irrigable, in the sense of [4], or not is addressed. A notion of irrigability dimension of a measure is given and lower and upper bounds are proved in terms of the minimal Hausdorff and respectively Minkowski dimension of a set on which the measure is concentrated. A notion of resolution dimension of a measure based on its discrete approximations is also introduced and its relation with the irrigation dimension is studiedI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
