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November 8th, 2016, 07:17 AM   #1
Glo
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Why is this relation with Hausdorff measure true?

I have found this formula:
$$\mathcal{H}^{n-m}(\{\lambda u| \;0<\lambda\leq\rho, u\in \mathbb{S}^{n-1} \})=\frac{\rho^{n-m}}{n-m} \int_{\mathbb{S}^n} d\mathcal{H}^{n-m-1}(u),$$

I think that this is a consequence of Fubini theorem, but I don't understand where the term $\frac{\rho^{n-m}}{n-m}$ come from.

I'm a bit confused. Can someone help me?

Thank you!
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