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Nearly all convex bodies are smooth and strictly convex. (English) Zbl 0607.52002
By an old result of V. Klee [Math. Ann. 139, 51-63 (1959; Zbl 0092.116)], those convex bodies which are not smooth or not strictly convex form a set of first Baire category. It is proved here that they are ”even fewer”: they only form a \(\sigma\)-porous set.

MSC:
52A05 Convex sets without dimension restrictions (aspects of convex geometry)
28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets
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References:
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