Theorems · Theorem · probability
ProbabilityTheory.Kernel.id_apply
∀ {α : Type u_1} {mα : MeasurableSpace α} (a : α), ProbabilityTheory.Kernel.id a = MeasureTheory.Measure.dirac a- Defined in
- Mathlib.Probability.Kernel.Basic
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 177 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.
- DFunLike.coestatement and proof · cited by 62,936
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- MeasureTheory.Measure.diracstatement and proof · cited by 210
- measurable_idproof · cited by 89
- ProbabilityTheory.Kernel.idstatement · cited by 72
- ProbabilityTheory.Kernel.deterministic_applyproof · cited by 15
Cited by15
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.compProd_applyproof · cited by 31
- ProbabilityTheory.Kernel.id_compproof · cited by 9
- ProbabilityTheory.Kernel.comp_idproof · cited by 8
- ProbabilityTheory.Kernel.parallelComp_id_left_comp_parallelCompproof · cited by 5
- ProbabilityTheory.Kernel.id_mapproof · cited by 3
- ProbabilityTheory.Kernel.traj_map_updateFinsetproof · cited by 3
- ProbabilityTheory.Kernel.id_comapproof · cited by 1
- MeasureTheory.Measure.prod_comp_rightproof · cited by 1
- ProbabilityTheory.Kernel.compProd_prodMkLeft_eq_compproof · cited by 1
- MeasureTheory.Measure.compProd_idproof · cited by 1
- ProbabilityTheory.Kernel.comp_parallelComp_comp_copyproof · cited by 0