Theorems · Theorem · real analysis

logDeriv_congr_nhdsNE

∀ {𝕜 : Type u_1} {𝕜' : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NontriviallyNormedField 𝕜']
  [inst_2 : NormedAlgebra 𝕜 𝕜'] {f g : 𝕜 → 𝕜'} {x : 𝕜},
  f =ᶠ[nhdsWithin x {x}ᶜ] g → logDeriv f =ᶠ[nhdsWithin x {x}ᶜ] logDeriv g

If two functions agree in a punctured neighborhood of x, then so do their logarithmic derivatives.

Defined in

Mathlib.Analysis.Calculus.LogDeriv

Cited by

2 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNontriviallyNormedFieldNormedAlgebra