Theorems · Definition · probability
ProbabilityTheory.Kernel.copy
(α : Type u_4) → [inst : MeasurableSpace α] → ProbabilityTheory.Kernel α (α × α)
The deterministic kernel that maps x : α to the Dirac measure at (x, x) : α × α.
- Defined in
- Mathlib.Probability.Kernel.Basic
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
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
- Function.diagproof · cited by 34
Cited by32
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.prodproof · cited by 65
- 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.copy_applystatement · cited by 6
- ProbabilityTheory.Kernel.compProd_defstatement and proof · cited by 5
- ProbabilityTheory.Kernel.parallelComp_comp_copystatement · cited by 3
- ProbabilityTheory.Kernel.parallelComp_comp_prodproof · cited by 3
- ProbabilityTheory.Kernel.lintegral_prodproof · cited by 3
- ProbabilityTheory.Kernel.swap_copystatement and proof · cited by 3
- ProbabilityTheory.Kernel.parallelComp_self_comp_copystatement · cited by 2
- ProbabilityTheory.parallelProd_posterior_comp_copy_compstatement and proof · cited by 2