# A Divergence Formula for Randomness and Dimension (Short Version)

@inproceedings{Lutz2009ADF,
title={A Divergence Formula for Randomness and Dimension (Short Version)},
author={Jack H. Lutz},
booktitle={CSP},
year={2009}
}
• J. H. Lutz
• Published in CSP 23 June 2009
• Computer Science, Mathematics
If $S$ is an infinite sequence over a finite alphabet $\Sigma$ and $\beta$ is a probability measure on $\Sigma$, then the {\it dimension} of $S$ with respect to $\beta$, written $\dim^\beta(S)$, is a constructive version of Billingsley dimension that coincides with the (constructive Hausdorff) dimension $\dim(S)$ when $\beta$ is the uniform probability measure. This paper shows that $\dim^\beta(S)$ and its dual $\Dim^\beta(S)$, the {\it strong dimension} of $S$ with respect to $\beta$, can be…
1 Citations

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