Theorems · Theorem · probability
ProbabilityTheory.Kernel.parallelComp_of_not_isSFiniteKernel_left
∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {δ : Type u_4} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
{mγ : MeasurableSpace γ} {mδ : MeasurableSpace δ} {κ : ProbabilityTheory.Kernel α β}
(η : ProbabilityTheory.Kernel γ δ), ¬ProbabilityTheory.IsSFiniteKernel κ → κ.parallelComp η = 0- Cited by
- 7 results in Mathlib
- Foundations
- Depth 222 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 and proof · cited by 1,281
- ProbabilityTheory.IsSFiniteKernelstatement and proof · cited by 248
- ProbabilityTheory.Kernel.parallelCompstatement · cited by 49
- ProbabilityTheory.Kernel.parallelComp_defproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.compProd_of_not_isSFiniteKernel_rightproof · cited by 8
- ProbabilityTheory.Kernel.parallelComp_id_left_comp_parallelCompproof · cited by 5
- ProbabilityTheory.Kernel.swap_parallelCompproof · cited by 4
- ProbabilityTheory.Kernel.parallelComp_sum_rightproof · cited by 1
- ProbabilityTheory.Kernel.parallelComp_zero_rightproof · cited by 1
- ProbabilityTheory.Kernel.parallelComp_commproof · cited by 1
- ProbabilityTheory.Kernel.prod_of_not_isSFiniteKernel_leftproof · cited by 0