Theorems · Theorem · functional analysis
NormedSpace.analyticAt_exp_of_mem_ball
∀ {𝕂 : Type u_1} {𝔸 : Type u_2} [inst : NontriviallyNormedField 𝕂] [inst_1 : NormedRing 𝔸] [inst_2 : NormedAlgebra 𝕂 𝔸]
[CompleteSpace 𝔸] [CharZero 𝕂],
∀ x ∈ Metric.eball 0 (NormedSpace.expSeries 𝕂 𝔸).radius, AnalyticAt 𝕂 NormedSpace.exp x- Cited by
- 4 results in Mathlib
- Foundations
- Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- ENNRealproof · cited by 9,879
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- CompleteSpacestatement and proof · cited by 2,532
- NormedAlgebrastatement and proof · cited by 1,165
- CharZerostatement and proof · cited by 932
- NormedRingstatement and proof · cited by 924
- AnalyticAtstatement · cited by 321
- Metric.eballstatement and proof · cited by 294
- pos_iff_ne_zeroproof · cited by 180
- NormedSpace.expstatement · cited by 157
- FormalMultilinearSeries.radiusstatement and proof · cited by 150
Cited by4
Results whose statement or proof uses this declaration.
- hasStrictFDerivAt_exp_smul_const_of_mem_ballproof · cited by 3
- NormedSpace.exp_analyticproof · cited by 2
- hasStrictFDerivAt_exp_of_mem_ballproof · cited by 2
- hasStrictFDerivAt_exp_smul_const_of_mem_ball'proof · cited by 2