On the dimension of an irrigable measure (Q2462217)

In this paper, the problem of determining if a given measure is irrigable, in the sense of \textit{F. Maddalena, S. Solimini} and \textit{J.-M. Morel} [Interfaces Free Bound. 5, No. 4, 391--415 (2003; Zbl 1057.35076)], 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.