Theorems · Theorem · probability
ProbabilityTheory.Kernel.bound_eq_one
∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} [Nonempty α]
(κ : ProbabilityTheory.Kernel α β) [ProbabilityTheory.IsMarkovKernel κ], κ.bound = 1- Defined in
- Mathlib.Probability.Kernel.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- MeasurableSpacestatement and proof · cited by 13,106
- ENNRealstatement · cited by 9,879
- iSupproof · cited by 2,415
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- MeasureTheory.IsProbabilityMeasure.measure_univproof · cited by 135
- ProbabilityTheory.IsMarkovKernelstatement and proof · cited by 124
- ciSup_constproof · cited by 43
- 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