1994/05/12 by Steprāns, Juris
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.math/9405201
This is a revision (and partial retraction) of my previous abstarct. Let λ(X) denote Lebesgue measure. If X⊆ [0,1] and r ∈ (0,1) then the r-Hausdorff capacity of X is denoted by Hr(X) and is defined to be the infimum of all ∑i=0^∞ λ(Ii)r where \Ii\i∈ω is a cover of X by intervals. The r Hausdorff capacity has the same null sets as the r-Hausdorff measure which is familiar from the theory of fractal dimension. It is shown that, given r < 1, it is possible to enlarge a model of set theory, V, by a generic extension V[G] so that the reals of V have Lebesgue measure zero but still have positive r-Hausdorff capacity.