Theorems · Theorem · complex analysis
FormalMultilinearSeries.summable_norm_mul_pow
∀ {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}, ↑r < p.radius → Summable fun n => ‖p n‖ * ↑r ^ n- Cited by
- 5 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- LT.lt.leproof · cited by 2,189
- SummationFilter.unconditionalstatement · cited by 2,068
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- NNReal.toRealstatement and proof · cited by 1,260
- Set.Iooproof · cited by 1,214
Cited by5
Results whose statement or proof uses this declaration.
- FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendstoproof · cited by 3
- FormalMultilinearSeries.summable_norm_applyproof · cited by 3
- HasFPowerSeriesWithinOnBall.tendsto_partialSum_prodproof · cited by 2
- FormalMultilinearSeries.ofScalars_radius_eq_zero_of_tendstoproof · cited by 1
- FormalMultilinearSeries.summable_nnnorm_mul_powproof · cited by 1