Theorems · Theorem · functional analysis
NormedSpace.norm_expSeries_summable_of_mem_ball
∀ {𝕂 : Type u_1} {𝔸 : Type u_2} [inst : NontriviallyNormedField 𝕂] [inst_1 : NormedRing 𝔸] [inst_2 : NormedAlgebra 𝕂 𝔸],
∀ x ∈ Metric.eball 0 (NormedSpace.expSeries 𝕂 𝔸).radius,
Summable fun n => ‖(NormedSpace.expSeries 𝕂 𝔸 n) fun x_1 => x‖- Cited by
- 4 results in Mathlib
- Foundations
- Depth 174 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.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Norm.normstatement · cited by 5,413
- SummationFilter.unconditionalstatement · cited by 2,068
- NormedAlgebrastatement and proof · cited by 1,165
- ContinuousMultilinearMapstatement · cited by 1,016
- NormedRingstatement and proof · cited by 924
- Summablestatement · cited by 778
- Metric.eballstatement and proof · cited by 294
- FormalMultilinearSeries.radiusstatement and proof · cited by 150
Cited by4
Results whose statement or proof uses this declaration.
- NormedSpace.norm_expSeries_summable_of_mem_ball'proof · cited by 3
- NormedSpace.norm_expSeries_div_summable_of_mem_ballproof · cited by 2
- NormedSpace.norm_expSeries_summableproof · cited by 1
- NormedSpace.expSeries_summable_of_mem_ballproof · cited by 0