Theorems · Theorem · probability
ProbabilityTheory.Kernel.bound_eq_zero_of_isEmpty
∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} [IsEmpty α]
(κ : ProbabilityTheory.Kernel α β), κ.bound = 0- Defined in
- Mathlib.Probability.Kernel.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- IsEmpty
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- MeasurableSpacestatement and proof · cited by 13,106
- ENNRealstatement · cited by 9,879
- Set.univproof · cited by 3,945
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- IsEmptystatement and proof · cited by 759
- bot_eq_zero'proof · cited by 92
- ciSup_of_emptyproof · cited by 23
- ProbabilityTheory.Kernel.boundstatement · cited by 17
Cited by4
Results whose statement or proof uses this declaration.
- ProbabilityTheory.bayesRisk_le_mul'proof · cited by 2
- ProbabilityTheory.Kernel.bound_le_oneproof · cited by 0
- ProbabilityTheory.avgRisk_le_mulproof · cited by 0
- ProbabilityTheory.bayesRisk_le_mulproof · cited by 0