Theorems · Theorem · real analysis
PiLp.hasStrictFDerivAt_ofLp
∀ {𝕜 : Type u_1} {ι : Type u_2} {E : ι → Type u_3} [inst : NontriviallyNormedField 𝕜]
[inst_1 : (i : ι) → NormedAddCommGroup (E i)] [inst_2 : (i : ι) → NormedSpace 𝕜 (E i)] [Finite ι] (p : ENNReal)
[Fact (1 ≤ p)] (f : PiLp p E), HasStrictFDerivAt WithLp.ofLp (↑(PiLp.continuousLinearEquiv p 𝕜 E)) f- Defined in
- Mathlib.Analysis.Calculus.FDeriv.WithLp
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 226 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- 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
- Fintypeproof · cited by 7,736
- nhdsproof · cited by 5,554
- Finitestatement and proof · cited by 3,029
- Factstatement and proof · cited by 2,726
- sub_selfproof · cited by 996
- ContinuousLinearEquiv.toContinuousLinearMapstatement · cited by 448
- WithLpstatement and proof · cited by 345
Cited by2
Results whose statement or proof uses this declaration.
- PiLp.hasStrictFDerivAt_applyproof · cited by 1
- PiLp.hasFDerivAt_ofLpproof · cited by 0