Theorems · Definition · functional analysis
BoundedContinuousFunction.nnrealPart
{α : Type u} → [inst : TopologicalSpace α] → BoundedContinuousFunction α ℝ → BoundedContinuousFunction α NNRealThe nonnegative part of a bounded continuous ℝ-valued function as a bounded
continuous ℝ≥0-valued function.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 157 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 and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- NNRealstatement · cited by 4,310
- BoundedContinuousFunctionstatement and proof · cited by 511
- Real.toNNRealproof · cited by 267
- BoundedContinuousFunction.compproof · cited by 12
Cited by6
Results whose statement or proof uses this declaration.
- MeasureTheory.FiniteMeasure.tendsto_iff_forall_integral_tendstoproof · cited by 3
- BoundedContinuousFunction.self_eq_nnrealPart_sub_nnrealPart_negstatement · cited by 1
- BoundedContinuousFunction.integral_eq_integral_nnrealPart_substatement and proof · cited by 1
- BoundedContinuousFunction.abs_self_eq_nnrealPart_add_nnrealPart_negstatement · cited by 0
- BoundedContinuousFunction.lintegral_of_real_lt_topproof · cited by 0
- BoundedContinuousFunction.nnrealPart_coeFn_eqstatement · cited by 0