Theorems · Theorem · functional analysis
CompactlySupportedContinuousMap.toReal_apply
∀ {α : Type u_2} [inst : TopologicalSpace α] (f : CompactlySupportedContinuousMap α NNReal) (x : α), f.toReal x = ↑(f x)- Cited by
- 12 results in Mathlib
- Foundations
- Depth 123 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- NNRealstatement and proof · cited by 4,310
- NNReal.toRealstatement · cited by 1,260
- CompactlySupportedContinuousMapstatement and proof · cited by 134
- CompactlySupportedContinuousMap.toRealstatement · cited by 15
- CompactlySupportedContinuousMap.compLeft_applyproof · cited by 1
Cited by12
Results whose statement or proof uses this declaration.
- NNRealRMK.integral_rieszMeasureproof · cited by 3
- CompactlySupportedContinuousMap.integralLinearMap_applystatement and proof · cited by 3
- RealRMK.rieszMeasure_le_of_eq_oneproof · cited by 3
- CompactlySupportedContinuousMap.nnrealPart_neg_toReal_eqproof · cited by 1
- CompactlySupportedContinuousMap.nnrealPart_sub_nnrealPart_negproof · cited by 1
- CompactlySupportedContinuousMap.nnrealPart_toReal_eqproof · cited by 1
- CompactlySupportedContinuousMap.toRealLinearMap_apply_applyproof · cited by 0
- NNRealRMK.integralLinearMap_rieszMeasureproof · cited by 0
- CompactlySupportedContinuousMap.toReal_addproof · cited by 0
- CompactlySupportedContinuousMap.toReal_nonnegproof · cited by 0
- CompactlySupportedContinuousMap.toReal_smulproof · cited by 0
- RealRMK.le_rieszMeasure_tsupport_subsetproof · cited by 0