Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-10T16:53:25.176Z Has data issue: false hasContentIssue false
  • English
  • Français

HAUSDORFF AND PACKING MEASURE OF SETS OF GENERIC POINTS: A ZERO-INFINITY LAW

Published online by Cambridge University Press:  29 March 2004

JIHUA MA  and
ZHIYING WEN
JIHUA MA
Affiliation:
Department of Mathematics, Wuhan University, Wuhan 430072, China Department of Mathematics, Friedrich-Schiller University, Jena D-07743, Germanylaoma2001@yahoo.com
ZHIYING WEN
Affiliation:
Department of Mathematics, Tsinghua University, Beijing 10084, Chinawenzy@tsinghua.edu.cn
Get access

Abstract

On the symbolic space endowed with a metric given by a Gibbs measure, it is shown that, for any invariant probability measure $\mu$ other than the given Gibbs measure, the set of $\mu$-generical points satisfies a ‘zero-infinity law’ (in particular, its Hausdorff and packing measure are infinite). This extends a result of R. Kaufman on Besicovitch–Eggleston sets, and applies to level sets of Birkhoff averages and certain subsets of self-similar sets.

Keywords

28A78 (primary)58F03 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 69 , Issue 2 , April 2004 , pp. 383 - 406
Copyright
The London Mathematical Society 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)