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.
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© 2010 Springer Science+Business Media, LLC
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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
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DOI: https://doi.org/10.1007/978-0-387-68441-3_13
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Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-95567-4
Online ISBN: 978-0-387-68441-3
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