Questions related to measures, sigma-algebras, measure spaces, Lebesgue integration and the like.

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Measure theory problem from Stein real analysis

Let $\mu$ be a Borel measure on the sphere $S^{d-1} = \{x \in \mathbb{R}^d:|x|=1\}$ which is rotation-invariant in the sense that $\mu(r(E)) = \mu(E),$ for every rotation $r$ of $\mathbb{R}^d$ and ...