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
Famous quotes containing the words statement of, statement and/or theorem:
“The most distinct and beautiful statement of any truth must take at last the mathematical form.”
—Henry David Thoreau (1817–1862)
“No statement about God is simply, literally true. God is far more than can be measured, described, defined in ordinary language, or pinned down to any particular happening.”
—David Jenkins (b. 1925)
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)