Theorems · Theorem · several complex variables
FormalMultilinearSeries.continuousOn_of_finite
∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [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) {n : ℕ}, (∀ (m : ℕ), n ≤ m → p m = 0) → Continuous p.sumThe sum of a finite power series is continuous.
- Defined in
- Mathlib.Analysis.Analytic.CPolynomialDef
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
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- Setproof · cited by 53,352
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Continuousstatement · cited by 2,592
- ContinuousOnproof · cited by 1,411
- ContinuousMultilinearMapstatement · cited by 1,016
- FormalMultilinearSeriesstatement and proof · cited by 615
- continuousOn_univproof · cited by 43
- FormalMultilinearSeries.sumstatement and proof · cited by 34
- Metric.eball_topproof · cited by 7
- FormalMultilinearSeries.hasFiniteFPowerSeriesOnBall_of_finiteproof · cited by 2
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