Theorems · Theorem · measure theory
BoundedContinuousFunction.apply_le_nndist_zero
∀ {X : Type u_1} [inst : TopologicalSpace X] (f : BoundedContinuousFunction X NNReal) (x : X), f x ≤ nndist 0 f- Cited by
- 2 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.
- DFunLike.coestatement and proof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- NNRealstatement and proof · cited by 4,310
- BoundedContinuousFunctionstatement and proof · cited by 511
- NNDist.nndiststatement and proof · cited by 235
- NNReal.nndist_zero_eq_valproof · cited by 2
- BoundedContinuousFunction.nndist_coe_le_nndistproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- BoundedContinuousFunction.apply_le_edist_zeroproof · cited by 1
- BoundedContinuousFunction.lintegral_le_edist_mulproof · cited by 1