Theorems · Theorem · complex analysis
FormalMultilinearSeries.le_radius_of_bound_nnreal
∀ {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) (C : NNReal) {r : NNReal}, (∀ (n : ℕ), ‖p n‖₊ * r ^ n ≤ C) → ↑r ≤ p.radiusIf ‖pₙ‖ rⁿ is bounded in n, then the radius of p is at least r.
- Cited by
- 3 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.
Cites13
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
- ENNRealstatement · cited by 9,879
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Norm.normproof · cited by 5,413
- NNRealstatement and proof · cited by 4,310
- ENNReal.ofNNRealstatement · cited by 1,279
- NNReal.toRealproof · cited by 1,260
- ContinuousMultilinearMapstatement · cited by 1,016
- NNNorm.nnnormstatement and proof · cited by 952
- FormalMultilinearSeriesstatement and proof · cited by 615
- FormalMultilinearSeries.radiusstatement · cited by 150
Cited by3
Results whose statement or proof uses this declaration.
- FormalMultilinearSeries.le_radius_of_summable_nnnormproof · cited by 3
- FormalMultilinearSeries.le_comp_radius_of_summableproof · cited by 1
- spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smulproof · cited by 1