Theorems · Theorem · probability
MeasureTheory.Measure.swap_comp
∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {μ : MeasureTheory.Measure (α × β)},
μ.bind ⇑(ProbabilityTheory.Kernel.swap α β) = MeasureTheory.Measure.map Prod.swap μ- Cited by
- 4 results in Mathlib
- Foundations
- Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 and proof · cited by 10,939
- ProbabilityTheory.Kernelstatement · cited by 1,281
- MeasureTheory.Measure.mapstatement · cited by 858
- MeasureTheory.Measure.bindstatement · cited by 173
- measurable_swapproof · cited by 42
- ProbabilityTheory.Kernel.swapstatement · cited by 27
- MeasureTheory.Measure.deterministic_comp_eq_mapproof · cited by 11
Cited by4
Results whose statement or proof uses this declaration.
- ProbabilityTheory.compProd_posterior_eq_swap_compproof · cited by 4
- ProbabilityTheory.ae_eq_posterior_of_compProd_eq_swap_compproof · cited by 3
- ProbabilityTheory.rnDeriv_posterior_ae_prodproof · cited by 1
- ProbabilityTheory.absolutelyContinuous_of_posteriorproof · cited by 1