Theorems · Theorem · measure theory
CompletelyRegularSpace.exists_BCNN
∀ {X : Type u_1} [inst : TopologicalSpace X] [CompletelyRegularSpace X] {K : Set X},
IsClosed K → ∀ {x : X}, x ∉ K → ∃ f, f x = 1 ∧ ∀ y ∈ K, f y = 0- Defined in
- Mathlib.MeasureTheory.Measure.DiracProba
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemproof · cited by 7,166
- NNRealstatement and proof · cited by 4,310
- LE.le.transproof · cited by 3,151
- one_mulproof · cited by 2,841
- Continuousproof · cited by 2,592
- IsClosedstatement and proof · cited by 1,639
- Dist.distproof · cited by 1,539
- unitIntervalproof · cited by 607
- Set.EqOnproof · cited by 603
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.not_tendsto_diracProba_of_not_tendstoproof · cited by 1