Generalized Hausdorff measure for generic compact sets

Balka, Richárd and Máthé, András (2013) Generalized Hausdorff measure for generic compact sets. ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 38. pp. 797-804. ISSN 1239-629X

Preview

Text 1204.1100v2.pdf Available under License Creative Commons Attribution. Download (162kB) | Preview

Abstract

Let X be a Polish space. We prove that the generic compact set K ⊆ X (in the sense of Baire category) is either finite or there is a continuous gauge function h such that 0 < Hh(K) < ∞, where Hh denotes the h-Hausdorff measure. This answers a question of C. Cabrelli, U. B. Darji, and U. M. Molter. Moreover, for every weak contraction f : K → X we have Hh (K ∩ f(K)) = 0. This is a measure theoretic analogue of a result of M. Elekes.

Actions (login required)

Edit Item