Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantization dimension and stability for infinite self-similar measures
  with respect to geometric mean error   Let $\mu$ be a Borel probability measure associated with an iterated function
system consisting of a countably infinite number of contracting similarities
and an infinite probability vector. In this paper, we study the quantization
dimension of the measure $\mu$ with respect to the geometric mean error. The
quantization for infinite systems is different from the well-known finite case
investigated by Graf and Luschgy. That is, many tools which are used in the
finite setting, for example, existence of finite maximal antichains, fail in
the infinite case. We prove that the quantization dimension of the measure
$\mu$ is equal to its Hausdorff dimension which extends a well-known result of
Graf and Luschgy for the finite case to an infinite setting. In the last
section, we discuss the stability of quantization dimension for infinite
systems.

20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex