Theorems · Definition · probability
ProbabilityTheory.Kernel.deterministic
{α : Type u_1} →
{β : Type u_2} →
{mα : MeasurableSpace α} → {mβ : MeasurableSpace β} → (f : α → β) → Measurable f → ProbabilityTheory.Kernel α βKernel which to a associates the dirac measure at f a. This is a Markov kernel.
- Defined in
- Mathlib.Probability.Kernel.Basic
- Cited by
- 57 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Measurablestatement and proof · cited by 1,499
- ProbabilityTheory.Kernelstatement · cited by 1,281
- MeasureTheory.Measure.diracproof · cited by 210
Cited by64
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.idproof · cited by 72
- ProbabilityTheory.Kernel.partialTrajproof · cited by 44
- ProbabilityTheory.Kernel.compProd_applyproof · cited by 31
- ProbabilityTheory.Kernel.copyproof · cited by 29
- ProbabilityTheory.Kernel.swapproof · cited by 27
- ProbabilityTheory.Kernel.deterministic_applystatement · cited by 15
- ProbabilityTheory.Kernel.compProd_of_not_isSFiniteKernel_leftproof · cited by 12
- MeasureTheory.Measure.deterministic_comp_eq_mapstatement · cited by 11
- ProbabilityTheory.Kernel.deterministic_comp_eq_mapstatement and proof · cited by 8
- ProbabilityTheory.Kernel.partialTraj_lestatement and proof · cited by 8
- ProbabilityTheory.Kernel.compProd_of_not_isSFiniteKernel_rightproof · cited by 8
- ProbabilityTheory.Kernel.discardproof · cited by 7