Cardinal Invariants Associated with Hausdorff Capacities

@inproceedings{Stepr1994CardinalIA,
title={Cardinal Invariants Associated with Hausdorff Capacities},
author={Juris Stepr and Ans},
year={1994}
}

Juris Stepr, Ans

Published 1994

Let λ(X) denote Lebesgue measure. If X ⊆ [0, 1] and r ∈ (0, 1) then the r-Hausdorff capacity of X is denoted by H r (X) and is defined to be the infimum of all ∞ i=0 λ(I i) r where {I i } 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… CONTINUE READING