Theorems · Theorem · complex analysis
FormalMultilinearSeries.le_radius_of_eventually_le
∀ {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]
(p : FormalMultilinearSeries 𝕜 E F) {r : NNReal} (C : ℝ),
(∀ᶠ (n : ℕ) in Filter.atTop, ‖p n‖ * ↑r ^ n ≤ C) → ↑r ≤ p.radius- Cited by
- 1 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · 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
- mul_oneproof · cited by 3,885
- Filter.Eventuallystatement and proof · cited by 3,134
- Filter.atTopstatement and proof · cited by 2,405
- ENNReal.ofNNRealstatement · cited by 1,279
- NNReal.toRealstatement and proof · cited by 1,260
Cited by1
Results whose statement or proof uses this declaration.
- FormalMultilinearSeries.radius_rightInv_pos_of_radius_posproof · cited by 1