Theorems · Theorem · complex analysis
AnalyticAt.frequently_zero_iff_eventually_zero
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {w : 𝕜},
AnalyticAt 𝕜 f w → ((∃ᶠ (z : 𝕜) in nhdsWithin w {w}ᶜ, f z = 0) ↔ ∀ᶠ (z : 𝕜) in nhds w, f z = 0)- Defined in
- Mathlib.Analysis.Analytic.IsolatedZeros
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 190 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.
- Setstatement · cited by 53,352
- 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
- Filter.Eventuallystatement and proof · cited by 3,134
- Compl.complstatement · cited by 2,925
- nhdsWithinstatement · cited by 1,912
- Filter.Frequentlystatement · cited by 414
- AnalyticAtstatement and proof · cited by 321
- nhdsWithin_le_nhdsproof · cited by 145
- Filter.Eventually.filter_monoproof · cited by 84
Cited by2
Results whose statement or proof uses this declaration.
- AnalyticAt.frequently_eq_iff_eventually_eqproof · cited by 6
- AnalyticOnNhd.eqOn_zero_of_preconnected_of_frequently_eq_zeroproof · cited by 6