Show that the n-dimensional Hausdorff measure of an $n$-dimensional cube is positive and finite. I can easily show that if it is finite then the $n+1$ dimensional measure is $0$ and the $n-1$ dimensional measure is $\infty$, but I'm not sure how to show that it is at exactly $n$ that the positive finite case occurs. Can anyone provide any tips?
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More detail for my comments from 2 years ago. Since the OP merely asked for "tips" I didn't provide a complete proof then.
you can use the relationship between Hausdorff n-dimensional measure and Lebesgue Measure . http://en.wikipedia.org/wiki/Hausdorff_measure