Cardinal Invariants Associated with Hausdorff Capacities

  title={Cardinal Invariants Associated with Hausdorff Capacities},
  author={Juris Stepr and Ans},
  • 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

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