Locatedness, Convexity, and Integrability in ${\mathbb{R}}^N$

We give an improved, detailed presentation of the constructive proof of the following corrected version of Theorem 2 of Locatedness, Convexity, and Lebesgue measurability: Let $\mathbf{S}$ be a Lebesgue integrable complemented set in ${\mathbb{R}}^N$ such that $\mu (\mathbf{S})>0$ and $S^1$ is both bounded and convex. Then $S^1$ is totally bounded and hence located in ${\mathbb{R}}^N$.