Theorems · Theorem · functional analysis
BoundedContinuousFunction.self_eq_nnrealPart_sub_nnrealPart_neg
∀ {α : Type u} [inst : TopologicalSpace α] (f : BoundedContinuousFunction α ℝ),
⇑f = NNReal.toReal ∘ ⇑f.nnrealPart - NNReal.toReal ∘ ⇑(-f).nnrealPartDecompose a bounded continuous function to its positive and negative parts.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 165 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 and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- NNRealstatement · cited by 4,310
- NNReal.toRealstatement · cited by 1,260
- BoundedContinuousFunctionstatement and proof · cited by 511
- max_zero_sub_max_neg_zero_eq_selfproof · cited by 6
- BoundedContinuousFunction.nnrealPartstatement · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- BoundedContinuousFunction.integral_eq_integral_nnrealPart_subproof · cited by 1