Theorems · Theorem · global analysis
HasFPowerSeriesOnBall.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} {f : E → F} {x : E} [CompleteSpace F],
HasFPowerSeriesOnBall f p x r → DifferentiableOn 𝕜 f (Metric.eball x r)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- CompleteSpacestatement and proof · cited by 2,532
- FormalMultilinearSeriesstatement and proof · cited by 615
- DifferentiableOnstatement · cited by 419
- Metric.eballstatement and proof · cited by 294
- HasFPowerSeriesOnBallstatement and proof · cited by 131
- AnalyticAt.differentiableWithinAtproof · cited by 5
- HasFPowerSeriesOnBall.analyticAt_of_memproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- HasFPowerSeriesAt.eventually_differentiableAtproof · cited by 0