Theorems · Definition · probability
ProbabilityTheory.Kernel.swap
(α : Type u_4) → (β : Type u_5) → [inst : MeasurableSpace α] → [inst_1 : MeasurableSpace β] → ProbabilityTheory.Kernel (α × β) (β × α)
The deterministic kernel that maps (x, y) to the Dirac measure at (y, x).
- Defined in
- Mathlib.Probability.Kernel.Basic
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 174 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
- ProbabilityTheory.Kernelstatement · cited by 1,281
- ProbabilityTheory.Kernel.deterministicproof · cited by 57
- measurable_swapproof · cited by 42
Cited by27
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.compProd_applyproof · cited by 31
- ProbabilityTheory.Kernel.compProd_of_not_isSFiniteKernel_leftproof · cited by 12
- ProbabilityTheory.Kernel.compProd_of_not_isSFiniteKernel_rightproof · cited by 8
- ProbabilityTheory.Kernel.compProd_defstatement and proof · cited by 5
- ProbabilityTheory.compProd_posterior_eq_swap_compstatement and proof · cited by 4
- ProbabilityTheory.Kernel.swap_parallelCompstatement and proof · cited by 4
- ProbabilityTheory.Kernel.swap_swapstatement · cited by 4
- MeasureTheory.Measure.swap_compstatement · cited by 4
- ProbabilityTheory.Kernel.swap_copystatement and proof · cited by 3
- ProbabilityTheory.ae_eq_posterior_of_compProd_eq_swap_compstatement and proof · cited by 3
- ProbabilityTheory.Kernel.parallelComp_id_right_comp_parallelCompproof · cited by 2
- ProbabilityTheory.parallelProd_posterior_comp_copy_compproof · cited by 2