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Algorithmic Dimension

  • Rodney G. Downey
  • Denis R. Hirschfeldt
Chapter
Part of the Theory and Applications of Computability book series (THEOAPPLCOM)

Abstract

Not all classes of measure 0 are created equal, and the classical theory of dimension provides a method for classifying them. Likewise, some nonrandom sets are more random than others. In this chapter, we look at effectivizations of Hausdorff dimension and other notions of dimension, and explore their relationships with calibrating randomness.

Keywords

Minimal Degree Initial Segment Kolmogorov Complexity Computable Dimension Packing Dimension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.School of Mathematics, Statistics and Operations ResearchVictoria University of WellingtonWellingtonNew Zealand
  2. 2.Department of MathematicsUniversity of ChicagoChicagoUSA

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