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Let   f   be an integrable log‐concave function on    R  n    with the center of mass at the origin. We show that∫  0  ∞   f   (  s  θ  )   d  s  ⩾   e   −  n∫   −  ∞   ∞   f   (  s  θ  )   d  sfor every    θ  ∈   S   n  −  1, and the constant    e   −  nis the best possible.

Grünbaum‐type inequality for log‐concave functions