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Infinite union of convex polytopes is till a polytope? (Union among probability simplex)
Answer to the Revised Question. Indeed, the union $P = \cup_{\mathbf{q}} A(\mathbf{q})$ is a polytope. To show this, let
$$ \tilde{P} = \texttt{ConvexHull}(\cup_{i=1}^{m} A(\mathbf{e}_i))$$
where $\...
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