Theorems · Theorem · complex analysis
FormalMultilinearSeries.le_radius_of_summable_norm
∀ {𝕜 : Type u_1} {E : Type u_3} {F : Type u_4} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {r : NNReal}
(p : FormalMultilinearSeries 𝕜 E F), (Summable fun n => ‖p n‖ * ↑r ^ n) → ↑r ≤ p.radius- Cited by
- 3 results in Mathlib
- Foundations
- Depth 168 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.
- Realstatement · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- ENNRealstatement · cited by 9,879
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Norm.normstatement and proof · cited by 5,413
- NNRealstatement and proof · cited by 4,310
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- ENNReal.ofNNRealstatement · cited by 1,279
- NNReal.toRealstatement and proof · cited by 1,260
- ContinuousMultilinearMapstatement · cited by 1,016
- Summablestatement and proof · cited by 778
Cited by3
Results whose statement or proof uses this declaration.
- FormalMultilinearSeries.inv_le_ofScalars_radius_of_tendstoproof · cited by 2
- FormalMultilinearSeries.radius_eq_top_of_summable_normproof · cited by 2
- FormalMultilinearSeries.not_summable_norm_of_radius_lt_nnnormproof · cited by 0