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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Downey, R.G., Hirschfeldt, D.R. (2010). Algorithmic Dimension. In: Algorithmic Randomness and Complexity. Theory and Applications of Computability. Springer, New York, NY. https://doi.org/10.1007/978-0-387-68441-3_13
Download citation
DOI: https://doi.org/10.1007/978-0-387-68441-3_13
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-95567-4
Online ISBN: 978-0-387-68441-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)