Statement of The Theorem
Let K be a convex body in n-dimensional Euclidean space Rn that is symmetric with respect to reflection in the origin, i.e. K = −K. Let f : Rn → R be a non-negative, symmetric, globally integrable function; i.e.
- f(x) ≥ 0 for all x ∈ Rn;
- f(x) = f(−x) for all x ∈ Rn;
Suppose also that the super-level sets L(f, t) of f, defined by
are convex subsets of Rn for every t ≥ 0. (This property is sometimes referred to as being unimodal.) Then, for any 0 ≤ c ≤ 1 and y ∈ Rn,
Read more about this topic: Anderson's Theorem
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