Theorems · Theorem · global analysis
HasFiniteFPowerSeriesOnBall.differentiableOn
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {F : Type v} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
{p : FormalMultilinearSeries 𝕜 E F} {r : ENNReal} {n : ℕ} {f : E → F} {x : E},
HasFiniteFPowerSeriesOnBall f p x n r → DifferentiableOn 𝕜 f (Metric.eball x r)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites11
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 and proof · cited by 9,879
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- FormalMultilinearSeriesstatement and proof · cited by 615
- DifferentiableOnstatement · cited by 419
- Metric.eballstatement and proof · cited by 294
- HasFiniteFPowerSeriesOnBallstatement and proof · cited by 46
- CPolynomialAt.analyticAtproof · cited by 7
- HasFiniteFPowerSeriesOnBall.cpolynomialAt_of_memproof · cited by 5
- AnalyticAt.differentiableWithinAtproof · cited by 5
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