Theorems · Theorem · several complex variables
AnalyticOnNhd.analyticOn
∀ {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] {f : E → F} {s : Set E},
AnalyticOnNhd 𝕜 f s → AnalyticOn 𝕜 f s- Defined in
- Mathlib.Analysis.Analytic.Basic
- Cited by
- 23 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · 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
- AnalyticOnNhdstatement and proof · cited by 206
- AnalyticOnstatement · cited by 161
- AnalyticAt.analyticWithinAtproof · cited by 19
Cited by23
Results whose statement or proof uses this declaration.
- contDiffOn_univproof · cited by 25
- AnalyticOnNhd.contDiffproof · cited by 7
- IsOpen.analyticOn_iff_analyticOnNhdproof · cited by 5
- AnalyticOnNhd.contDiffOnproof · cited by 2
- analyticOn_constproof · cited by 2
- ProbabilityTheory.analyticOn_cgfproof · cited by 1
- AnalyticOnNhd.contDiffOn_of_completeSpaceproof · cited by 1
- analyticOn_sigmoidproof · cited by 1
- ContinuousMultilinearMap.analyticOn_uncurry_of_linearproof · cited by 1
- AnalyticWithinAt.exists_hasFTaylorSeriesUpToOnproof · cited by 1
- LSeries_analyticOnproof · cited by 0
- ProbabilityTheory.analyticOn_complexMGFproof · cited by 0