Theorems · Theorem · probability
MeasureTheory.Measure.compProd_eq_zero_iff
∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {μ : MeasureTheory.Measure α}
{κ : ProbabilityTheory.Kernel α β} [MeasureTheory.SFinite μ] [ProbabilityTheory.IsSFiniteKernel κ],
μ.compProd κ = 0 ↔ ∀ᵐ (a : α) ∂μ, κ a = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 229 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealproof · cited by 9,879
- Set.univproof · cited by 3,945
- Filter.Eventuallystatement and proof · cited by 3,134
- MeasureTheory.aestatement and proof · cited by 2,352
- SProd.sprodproof · cited by 1,750
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- MeasureTheory.SFinitestatement and proof · cited by 449
- ProbabilityTheory.IsSFiniteKernelstatement and proof · cited by 248
- MeasurableSet.univproof · cited by 178
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.AbsolutelyContinuous.kernel_of_compProdproof · cited by 5