Theorems · Definition · functional analysis
CompactlySupportedContinuousMap.toReal
{α : Type u_2} →
[inst : TopologicalSpace α] → CompactlySupportedContinuousMap α NNReal → CompactlySupportedContinuousMap α ℝThe compactly supported continuous ℝ≥0-valued function as a compactly supported ℝ-valued
function.
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 122 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- NNRealstatement and proof · cited by 4,310
- CompactlySupportedContinuousMapstatement and proof · cited by 134
- ContinuousMap.coeNNRealRealproof · cited by 3
- CompactlySupportedContinuousMap.compLeftproof · cited by 3
Cited by16
Results whose statement or proof uses this declaration.
- CompactlySupportedContinuousMap.toReal_applystatement · cited by 12
- CompactlySupportedContinuousMap.toRealLinearMapproof · cited by 4
- NNRealRMK.integral_rieszMeasureproof · cited by 3
- CompactlySupportedContinuousMap.integralLinearMap_applystatement and proof · cited by 3
- RealRMK.rieszMeasure_le_of_eq_oneproof · cited by 3
- CompactlySupportedContinuousMap.eq_toRealPositiveLinear_toRealstatement · cited by 2
- CompactlySupportedContinuousMap.nnrealPart_neg_toReal_eqstatement · cited by 1
- CompactlySupportedContinuousMap.nnrealPart_sub_nnrealPart_negstatement · cited by 1
- CompactlySupportedContinuousMap.nnrealPart_toReal_eqstatement · cited by 1
- CompactlySupportedContinuousMap.toNNRealLinear_applystatement · cited by 1
- CompactlySupportedContinuousMap.toRealLinearMap_applystatement · cited by 0
- CompactlySupportedContinuousMap.toReal_addstatement · cited by 0