Theorems · Theorem · complex analysis
FormalMultilinearSeries.summable_nnnorm_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
- 1 results in Mathlib
- Foundations
- Depth 173 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.
- 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
- NNRealstatement and proof · cited by 4,310
- SummationFilter.unconditionalstatement · cited by 2,068
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- ContinuousMultilinearMapstatement · cited by 1,016
- NNNorm.nnnormstatement · cited by 952
- Summablestatement · cited by 778
- FormalMultilinearSeriesstatement and proof · cited by 615
- FormalMultilinearSeries.radiusstatement and proof · cited by 150
Cited by1
Results whose statement or proof uses this declaration.
- FormalMultilinearSeries.changeOriginSeries_summable_aux₁proof · cited by 3