Theorems · Theorem · probability
ProbabilityTheory.Kernel.withDensity_tsum
∀ {α : Type u_1} {β : Type u_2} {ι : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} [inst : Countable ι]
(κ : ProbabilityTheory.Kernel α β) [inst_1 : ProbabilityTheory.IsSFiniteKernel κ] {f : ι → α → β → ENNReal},
(∀ (i : ι), Measurable (Function.uncurry (f i))) →
κ.withDensity (∑' (n : ι), f n) = ProbabilityTheory.Kernel.sum fun n => κ.withDensity (f n)- Defined in
- Mathlib.Probability.Kernel.WithDensity
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites34
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- TopologicalSpaceproof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- AddCommMonoidproof · cited by 12,281
- MeasureTheory.Measureproof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- MeasurableSetproof · cited by 3,075
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- MeasureTheory.Measure.restrictproof · cited by 1,646
- Measurablestatement and proof · cited by 1,499
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.isSFiniteKernel_withDensity_of_isFiniteKernelproof · cited by 0