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2 votes
1 answer
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Examples of "almost" Ahlfors regular measures

Let $\mu$ be a Borel probability measure on $\mathbb{R}^n$ such that there are $c,C,d,D>0$ satisfying: for every $x \in \mathbb{R}^n$ and every $r>0$ $$ c r^d \leq \mu(B(x,r)) \leq Cr^D. $$ Let'...
1 vote
0 answers
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Measure of the boundary of the support of a certain function defined by an expectation

Suppose: $\mathcal{S} = \{ S \in \mathbb{R}^d \ | \ S_i > 0, \forall i = 1,...,d \} $ $R$ is a random vector (on some probability space, $\Omega$) such that, $R: \Omega \to \mathcal{S}$. $h : ...