Theorems · Theorem · complex analysis
analyticOrderAt_congr
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {f g : 𝕜 → E} {z₀ : 𝕜}, f =ᶠ[nhds z₀] g → analyticOrderAt f z₀ = analyticOrderAt g z₀If two functions agree in a neighborhood of z₀, then their orders at z₀ agree.
- Defined in
- Mathlib.Analysis.Analytic.Order
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- nhdsstatement and proof · cited by 5,554
- ENatstatement and proof · cited by 4,985
- Filter.Eventuallyproof · cited by 3,134
- Filter.EventuallyEqstatement and proof · cited by 1,912
- Filter.EventuallyEq.symmproof · cited by 408
- AnalyticAtproof · cited by 321
- analyticOrderAtstatement and proof · cited by 69
- AnalyticAt.congrproof · cited by 12
- analyticOrderAt_of_not_analyticAtproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- AnalyticAt.analyticOrderAt_deriv_add_oneproof · cited by 2