A Divergence Formula for Randomness and Dimension (Short Version)
نویسنده
چکیده
If S is an infinite sequence over a finite alphabet Σ and β is a probability measure on Σ, then the dimension of S with respect to β , written dimβ (S), is a constructive version of Billingsley dimension that coincides with the (constructive Hausdorff) dimension dim(S) when β is the uniform probability measure. This paper shows that dimβ (S) and its dual Dimβ (S), the strong dimension of S with respect to β , can be used in conjunction with randomness to measure the similarity of two probability measures α and β on Σ. Specifically, we prove that the divergence formula
منابع مشابه
A Divergence Formula for Randomness and Dimension
If S is an infinite sequence over a finite alphabet Σ and β is a probability measure on Σ, then the dimension of S with respect to β, written dim(S), is a constructive version of Billingsley dimension that coincides with the (constructive Hausdorff) dimension dim(S) when β is the uniform probability measure. This paper shows that dim(S) and its dual Dim(S), the strong dimension of S with respec...
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