Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homogeneous probability measures on the Cantor set   We show that every homeomorphism between closed measure zero subsets extends
to a measure preserving auto-homeomorphism, whenever the Cantor set is endowed
with a suitable probability measure. This is valid both for the standard
product measure, as well as for the universal homogeneous rational measure.

7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an