Hausdorff-dimension of non measurable sets?

They key word here is the 'outer'. Start with a fixed dimension. If you define Hausdorff-outer-measure you are taking a limit of sets that all contain your original set. So if the original set is not measurable, the Hausdorff-outer-measure will give you the size of the smallest measurable set that contains your original set.

When you compute the Hausdorff dimension you still get the dimension of some limit of measurable sets that contain your original set.

Tags:

Measure Theory

Hausdorff Dimension

Hausdorff Measure

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