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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 : ...
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