Theorems · Definition · probability
ProbabilityTheory.Kernel.sum
{α : Type u_1} →
{β : Type u_2} →
{ι : Type u_3} →
{mα : MeasurableSpace α} →
{mβ : MeasurableSpace β} → [Countable ι] → (ι → ProbabilityTheory.Kernel α β) → ProbabilityTheory.Kernel α βSum of an indexed family of kernels.
- Defined in
- Mathlib.Probability.Kernel.Defs
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Countable
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.
- DFunLike.coeproof · cited by 62,936
- MeasurableSpacestatement and proof · cited by 13,106
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- Countablestatement and proof · cited by 633
- MeasureTheory.Measure.sumproof · cited by 121
Cited by33
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.measurable_kernel_prodMk_leftproof · cited by 12
- ProbabilityTheory.Kernel.sum.congr_simpstatement and proof · cited by 10
- ProbabilityTheory.Kernel.kernel_sum_seqstatement · cited by 6
- ProbabilityTheory.Kernel.sum_apply'statement · cited by 6
- ProbabilityTheory.Kernel.sum_zerostatement · cited by 6
- ProbabilityTheory.Kernel.sum_applystatement · cited by 4
- ProbabilityTheory.Kernel.comp_sum_leftstatement and proof · cited by 2
- ProbabilityTheory.Kernel.comp_sum_rightstatement and proof · cited by 2
- ProbabilityTheory.Kernel.withDensity_kernel_sumstatement and proof · cited by 1
- ProbabilityTheory.Kernel.withDensity_tsumstatement · cited by 1
- ProbabilityTheory.Kernel.parallelComp_sum_leftstatement and proof · cited by 1
- ProbabilityTheory.Kernel.parallelComp_sum_rightstatement and proof · cited by 1