Göteborgs universitets publikationer

# Exact Hausdorff Measures of Cantor Sets

Författare och institution:
Malin Palö Forsström (Institutionen för matematiska vetenskaper, matematisk statistik, Chalmers/GU)
Real Analysis Exchange, 39 ( 2 ) s. 367-384
ISSN:
0147-1937
E-ISSN:
1930-1219
Publikationstyp:
Publiceringsår:
2014
Språk:
engelska
Fulltextlänk:
Sammanfattning (abstract):
Cantor sets in R are common examples of sets for which Hausdorff measures can be positive and fnite. However, there exist Cantor sets for which no Hausdorff measure is supported and finite. The purpose of this paper is to try to resolve this problem by studying an extension of the Hausdorff measures $\mu_h$ on on $\mathbb{R}$, allowing gauge functions to depend on the midpoint of the covering intervals instead of only on the diameter. As a main result, a theorem about the Hausdorff measure of any regular enough Cantor set, with respect to a chosen gauge function, is obtained.
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
NATURVETENSKAP ->
Matematik ->
Matematisk analys
NATURVETENSKAP ->
Matematik ->
Diskret matematik
Chalmers fundament:
Grundläggande vetenskaper
Postens nummer:
206628