Abstract
Let $X_1, X_2, \cdots$ be a sequence of independent identically distributed random vectors in $R^n$ (Euclidean $n$-space). Let the $X_i$'s have a distribution which is a product of $n$ Borel probability measures along an orthogonal set of axes. After sampling $m$ times let $H_m$ be the convex hull of $\{X_1, \cdots, X_m\}$. All possible limiting shapes for $H_m$ are found along with necessary and sufficient conditions that the limit be obtained.
Citation
Lloyd Fisher. "Limiting Sets and Convex Hulls of Samples from Product Measures." Ann. Math. Statist. 40 (5) 1824 - 1832, October, 1969. https://doi.org/10.1214/aoms/1177697395
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