Theorems · Theorem · probability
ProbabilityTheory.Kernel.swap_apply
∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} (ab : α × β),
(ProbabilityTheory.Kernel.swap α β) ab = MeasureTheory.Measure.dirac ab.swapSee swap_apply' for a fully applied version of this lemma.
- Defined in
- Mathlib.Probability.Kernel.Basic
- Cited by
- 2 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_swapproof · cited by 42
- ProbabilityTheory.Kernel.swapstatement · cited by 27
- ProbabilityTheory.Kernel.deterministic_applyproof · cited by 15
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.swap_parallelCompproof · cited by 4
- ProbabilityTheory.Kernel.swap_apply'proof · cited by 2