Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A sequential view of self--similar measures, or, What the ghosts of
  Mahler and Cantor can teach us about dimension   We show that missing $q$-ary digit sets $F\subseteq[0,1]$ have corresponding
naturally associated countable binary $q$-automatic sequence $f$. Using this
correspondence, we show that the Hausdorff dimension of $F$ is equal to the
base-$q$ logarithm of the Mahler eigenvalue of $f$. In addition, we demonstrate
that the standard mass distribution $\nu_F$ supported on $F$ is equal to the
ghost measure $\mu_f$ of $f$.

25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat