Theorems · Theorem · functional analysis
CompactlySupportedContinuousMap.eq_toRealPositiveLinear_toReal
∀ {α : Type u_2} [inst : TopologicalSpace α] (Λ : CompactlySupportedContinuousMap α NNReal →ₗ[NNReal] NNReal)
(f : CompactlySupportedContinuousMap α NNReal),
(CompactlySupportedContinuousMap.toRealPositiveLinear Λ) f.toReal = ↑(Λ f)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- RingHom.idstatement and proof · cited by 18,349
- LinearMapstatement and proof · cited by 10,215
- NNRealstatement and proof · cited by 4,310
- map_zeroproof · cited by 1,614
- NNReal.toRealstatement and proof · cited by 1,260
- sub_zeroproof · cited by 938
- CompactlySupportedContinuousMapstatement and proof · cited by 134
- PositiveLinearMapstatement · cited by 52
- CompactlySupportedContinuousMap.toRealstatement · cited by 15
Cited by2
Results whose statement or proof uses this declaration.
- NNRealRMK.integral_rieszMeasureproof · cited by 3
- CompactlySupportedContinuousMap.eq_toNNRealLinear_toRealPositiveLinearproof · cited by 1