Theorems · Theorem · functional analysis
cfc_nnreal_eq_real
∀ {A : Type u_1} [inst : TopologicalSpace A] [inst_1 : Ring A] [inst_2 : PartialOrder A] [inst_3 : StarRing A]
[inst_4 : StarOrderedRing A] [inst_5 : Algebra ℝ A] [IsSemitopologicalRing A] [T2Space A]
[inst_8 : ContinuousFunctionalCalculus ℝ A IsSelfAdjoint] [inst_9 : NonnegSpectrumClass ℝ A] (f : NNReal → NNReal)
(a : A), autoParam (0 ≤ a) cfc_nnreal_eq_real._auto_1 → cfc f a = cfc (fun x => ↑(f x.toNNReal)) a- Cited by
- 9 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- NNRealstatement and proof · cited by 4,310
- StarRingstatement and proof · cited by 1,686
- T2Spacestatement and proof · cited by 1,351
- NNReal.toRealstatement · cited by 1,260
- StarOrderedRingstatement and proof · cited by 587
- IsSelfAdjointstatement and proof · cited by 545
- ContinuousFunctionalCalculusstatement and proof · cited by 331
Cited by9
Results whose statement or proof uses this declaration.
- IsGreatest.nnnorm_cfc_nnrealproof · cited by 5
- CFC.rpow_eq_cfc_realproof · cited by 2
- continuousOn_cfc_nnrealproof · cited by 2
- range_cfc_nnreal_eq_image_cfc_realproof · cited by 2
- cfc_real_eq_nnrealproof · cited by 1
- cfc_tsubproof · cited by 1
- cfc_nnreal_le_iffproof · cited by 0
- Commute.cfc_nnrealproof · cited by 0
- Matrix.PosSemidef.det_sqrtproof · cited by 0