Effective Dimension - Comparison To Classical Dimension

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 .

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