Comparison To Classical Dimension
If Z is a subset of 2ω, its Hausdorff dimension is .
The packing dimension of Z is .
Thus the effective Hausdorff and packing dimensions of a set are simply the classical Hausdorff and packing dimensions of (respectively) when we restrict our attention to c.e. gales.
Define the following:
A consequence of the above is that these all have Hausdorff dimension .
and all have packing dimension 1.
and all have packing dimension .
Read more about this topic: Effective Dimension
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