Theorems · Theorem · functional analysis
CompactlySupportedContinuousMap.nnrealPart_neg_toReal_eq
∀ {α : Type u_2} [inst : TopologicalSpace α] (f : CompactlySupportedContinuousMap α NNReal), (-f.toReal).nnrealPart = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 124 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.
Cites12
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
- NNReal.toRealproof · cited by 1,260
- Real.toNNRealproof · cited by 267
- NNReal.eqproof · cited by 201
- sup_of_le_rightproof · cited by 143
- CompactlySupportedContinuousMapstatement and proof · cited by 134
- CompactlySupportedContinuousMap.toRealstatement · cited by 15
- CompactlySupportedContinuousMap.extproof · cited by 15
- CompactlySupportedContinuousMap.nnrealPartstatement · cited by 15
- CompactlySupportedContinuousMap.toReal_applyproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- CompactlySupportedContinuousMap.eq_toRealPositiveLinear_toRealproof · cited by 2