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

Douglas S Bridges

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

Classical Analysis and ODEs 2026-07-17 v1 Logic

Authors: Douglas S Bridges

Abstract

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 $\mathbb{R}^N$ .

Cite

@article{arxiv.2607.15558,
  title  = {Locatedness, Convexity, and Integrability in $\mathbb{R}^N$},
  author = {Douglas S Bridges},
  journal= {arXiv preprint arXiv:2607.15558},
  year   = {2026}
}