Powers of extended nonnegative reals to a sum #
A power of an extended nonnegative real to a sum of nonnegative exponents is the product of the powers, as for the reals.
[UPSTREAM] candidate for Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean, beside
ENNReal.prod_rpow_of_nonneg.
theorem
ENNReal.rpow_sum_of_nonneg
{ι : Type u_1}
{s : Finset ι}
{w : ι → ℝ}
(x : ENNReal)
(hw : ∀ i ∈ s, 0 ≤ w i)
:
x ^ ∑ i ∈ s, w i = ∏ i ∈ s, x ^ w i