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In convex analysis, a non-negative function f : R → R+ is logarithmically concave if its domain is a convex set, and if it satisfies the inequality
for all x,y ∈ dom f and 0 < θ < 1. If f is strictly positive, this is equivalent to saying that the logarithm of the function, log ∘ f, is concave; that is,
for all x,y ∈ dom f and 0 < θ < 1.
Examples of log-concave functions are the 0-1 indicator functions of convex sets , and the Gaussian function.
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