Theorems · Theorem · complex analysis
HasFPowerSeriesAt.eq_zero_of_eventually
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {p : FormalMultilinearSeries 𝕜 𝕜 E} {f : 𝕜 → E} {x : 𝕜},
HasFPowerSeriesAt f p x → f =ᶠ[nhds x] 0 → p = 0A one-dimensional formal multilinear series representing a locally zero function is zero.
- Defined in
- Mathlib.Analysis.Analytic.Uniqueness
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Filter.EventuallyEqstatement and proof · cited by 1,912
- FormalMultilinearSeriesstatement and proof · cited by 615
- HasFPowerSeriesAtstatement and proof · cited by 94
- HasFPowerSeriesAt.congrproof · cited by 6
- HasFPowerSeriesAt.eq_zeroproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- HasFPowerSeriesAt.locally_zero_iffproof · cited by 1