Real.geom_mean_le_arith_mean_weighted

∀ {ι : Type u} (s : Finset ι) (w z : ι → ℝ),
  (∀ i ∈ s, 0 ≤ w i) → ∑ i ∈ s, w i = 1 → (∀ i ∈ s, 0 ≤ z i) → ∏ i ∈ s, z i ^ w i ≤ ∑ i ∈ s, w i * z i

AM-GM inequality: The geometric mean is less than or equal to the arithmetic mean, weighted version for real-valued nonnegative functions.

Defined in: Mathlib.Analysis.MeanInequalities
Cited by: 5 results in Mathlib
Foundations: Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound

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