Theorems · Theorem · real analysis

Finsupp.log_prod

∀ {α : Type u_1} {β : Type u_2} [inst : Zero β] (f : α →₀ β) (g : α → β → ℝ),
  (∀ (a : α), g a (f a) = 0 → f a = 0) → Real.log (f.prod g) = f.sum fun a b => Real.log (g a b)

Defined in

Mathlib.Analysis.SpecialFunctions.Log.Basic

Cited by

1 results in Mathlib

Foundations

Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Zero