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Answer by Joseph O'Rourke for The (Sigma) Algebra of Convex Sets
This is tangential to the posed question, not an answer. But there has been work on adiscrete version of this concept, called in the literature the convex deficiency tree.For example, here is Fig. 1...
View ArticleAnswer by Michael Greinecker for The (Sigma) Algebra of Convex Sets
The answer to the second question is yes. Trivially, every closed convex set is closed and hence in the Borel $\sigma$-algebra as the complement of an open set.For the other direction, note that every...
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The (Sigma) Algebra of Convex Sets
This is a question-by-proxy for a colleague from computer science. I'm sure many people here are already aware that convex decomposition forms an important sub-field of both computational geometry and...
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