Theorems · Definition · probability
ProbabilityTheory.Kernel.bound
{α : Type u_1} →
{β : Type u_2} → {mα : MeasurableSpace α} → {mβ : MeasurableSpace β} → ProbabilityTheory.Kernel α β → ENNRealA constant C : ℝ≥0∞ such that C < ∞ for a finite kernel
(ProbabilityTheory.IsFiniteKernel.bound_lt_top κ) and for all a : α and s : Set β,
κ a s ≤ C (ProbabilityTheory.Kernel.measure_le_bound κ a s).
- Defined in
- Mathlib.Probability.Kernel.Defs
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- DFunLike.coeproof · cited by 62,936
- MeasurableSpacestatement and proof · cited by 13,106
- ENNRealstatement · cited by 9,879
- Set.univproof · cited by 3,945
- iSupproof · cited by 2,415
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
Cited by17
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.measure_le_boundstatement · cited by 6
- ProbabilityTheory.Kernel.bound_eq_onestatement · cited by 4
- ProbabilityTheory.Kernel.bound_eq_zero_of_isEmptystatement · cited by 4
- ProbabilityTheory.Kernel.bound_lt_topstatement · cited by 4
- ProbabilityTheory.avgRisk_le_mul'statement and proof · cited by 2
- ProbabilityTheory.bayesRisk_le_mul'statement and proof · cited by 2
- ProbabilityTheory.Kernel.bound_eq_zero_of_isEmpty'statement · cited by 2
- ProbabilityTheory.Kernel.IsFiniteKernel.integrableproof · cited by 1
- ProbabilityTheory.Kernel.bound_ne_topstatement · cited by 1
- ProbabilityTheory.Kernel.bound_zerostatement · cited by 1
- ProbabilityTheory.avgRisk_le_mulproof · cited by 0
- ProbabilityTheory.Kernel.isFiniteKernel_withDensity_of_boundedproof · cited by 0