Theorems · Definition · functional analysis
CompactlySupportedContinuousMap.nnrealPart
{α : Type u_2} →
[inst : TopologicalSpace α] → CompactlySupportedContinuousMap α ℝ → CompactlySupportedContinuousMap α NNRealThe nonnegative part of a continuous compactly supported ℝ-valued function as a
continuous compactly supported ℝ≥0-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.
Cites7
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
- NNRealstatement · cited by 4,310
- Real.toNNRealproof · cited by 267
- CompactlySupportedContinuousMapstatement and proof · cited by 134
- ContinuousMap.toFunproof · cited by 72
- CompactlySupportedContinuousMap.toContinuousMapproof · cited by 10
Cited by16
Results whose statement or proof uses this declaration.
- CompactlySupportedContinuousMap.toRealPositiveLinearproof · cited by 4
- rieszContentAux_image_nonemptyproof · cited by 3
- RealRMK.rieszMeasure_le_of_eq_oneproof · cited by 3
- MeasureTheory.Measure.ext_of_integral_eq_on_compactlySupported_nnrealproof · cited by 2
- CompactlySupportedContinuousMap.nnrealPart_neg_toReal_eqstatement · cited by 1
- CompactlySupportedContinuousMap.nnrealPart_sub_nnrealPart_negstatement and proof · cited by 1
- CompactlySupportedContinuousMap.nnrealPart_toReal_eqstatement · cited by 1
- exists_continuous_add_one_of_isCompact_nnrealproof · cited by 1
- CompactlySupportedContinuousMap.nnrealPart_add_le_add_nnrealPartstatement · cited by 1
- CompactlySupportedContinuousMap.nnrealPart_neg_eq_zero_of_nonnegstatement · cited by 0
- CompactlySupportedContinuousMap.exists_add_nnrealPart_add_eqstatement and proof · cited by 0
- CompactlySupportedContinuousMap.nnrealPart_smul_negstatement · cited by 0