Theorems · Theorem · probability
ProbabilityTheory.Kernel.fst_apply
∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
{mγ : MeasurableSpace γ} (κ : ProbabilityTheory.Kernel α (β × γ)) (a : α),
κ.fst a = MeasureTheory.Measure.map Prod.fst (κ a)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 · cited by 10,939
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- MeasureTheory.Measure.mapstatement · cited by 858
- ProbabilityTheory.Kernel.fststatement · cited by 81
Cited by5
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.fst_apply'proof · cited by 10
- ProbabilityTheory.Kernel.fst_prodproof · cited by 2
- MeasureTheory.Measure.fst_compProdproof · cited by 2
- ProbabilityTheory.Kernel.apply_eq_measure_condKernel_of_compProd_eqproof · cited by 2