Theorems · Theorem · probability
ProbabilityTheory.Kernel.deterministic_apply
∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {f : α → β} (hf : Measurable f)
(a : α), (ProbabilityTheory.Kernel.deterministic f hf) a = MeasureTheory.Measure.dirac (f a)- Defined in
- Mathlib.Probability.Kernel.Basic
- Cited by
- 15 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement · cited by 10,939
- Measurablestatement and proof · cited by 1,499
- ProbabilityTheory.Kernelstatement · cited by 1,281
- MeasureTheory.Measure.diracstatement · cited by 210
- ProbabilityTheory.Kernel.deterministicstatement · cited by 57
Cited by15
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.compProd_applyproof · cited by 31
- ProbabilityTheory.Kernel.id_applyproof · cited by 15
- ProbabilityTheory.Kernel.lintegral_deterministic'proof · cited by 5
- ProbabilityTheory.Kernel.discard_applyproof · cited by 3
- ProbabilityTheory.Kernel.id_mapproof · cited by 3
- ProbabilityTheory.Kernel.swap_applyproof · cited by 2
- ProbabilityTheory.Kernel.id_comapproof · cited by 1
- ProbabilityTheory.Kernel.borelMarkovFromReal_applyproof · cited by 1
- ProbabilityTheory.Kernel.setLIntegral_deterministicproof · cited by 0
- ProbabilityTheory.Kernel.setLIntegral_deterministic'proof · cited by 0
- ProbabilityTheory.Kernel.setIntegral_deterministicproof · cited by 0
- ProbabilityTheory.Kernel.setIntegral_deterministic'proof · cited by 0