# 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} }

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…

## One Citation

### A divergence formula for randomness and dimension

- Computer Science, MathematicsTheor. Comput. Sci.
- 2008

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