Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact Hausdorff measures of Cantor sets   Cantor sets in \(\mathbb{R}\) are common examples of sets for which Hausdorff
measures can be positive and finite. 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 \(\mathbb{R}\), 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.

30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga