add_concaveOn — Mathlib

English

If f is strictly concave on s and g is concave on s, then f + g is strictly concave on s.

Русский

Если f строго вогнутая на s и g вогнутая на s, то f+g строго вогнутая на s.

LaTeX

$$$\text{If } f\text{ is strictly concave on } s\text{ and } g\text{ is concave on } s,\; f+g\text{ is strictly concave on } s$$$

Lean4

theorem add_concaveOn (hf : StrictConcaveOn 𝕜 s f) (hg : ConcaveOn 𝕜 s g) : StrictConcaveOn 𝕜 s (f + g) :=
  hf.dual.add_convexOn hg.dual

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