Theorems · Theorem · probability
ProbabilityTheory.Kernel.sum.congr_simp
∀ {α : Type u_1} {β : Type u_2} {ι : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} [inst : Countable ι]
(κ κ_1 : ι → ProbabilityTheory.Kernel α β),
κ = κ_1 → ProbabilityTheory.Kernel.sum κ = ProbabilityTheory.Kernel.sum κ_1- Defined in
- Mathlib.Probability.Kernel.Defs
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 195 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.
Cites4
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
- Countablestatement and proof · cited by 633
- ProbabilityTheory.Kernel.sumstatement and proof · cited by 31
Cited by10
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.withDensity_kernel_sumproof · cited by 1
- ProbabilityTheory.Kernel.compProd_eq_sum_compProdproof · cited by 1
- ProbabilityTheory.Kernel.parallelComp_sum_leftproof · cited by 1
- ProbabilityTheory.Kernel.parallelComp_sum_rightproof · cited by 1
- ProbabilityTheory.Kernel.compProd_sum_leftproof · cited by 1
- ProbabilityTheory.Kernel.compProd_sum_rightproof · cited by 1
- ProbabilityTheory.Kernel.compProd_eq_sum_compProd_leftproof · cited by 0
- ProbabilityTheory.Kernel.compProd_eq_sum_compProd_rightproof · cited by 0
- ProbabilityTheory.Kernel.sum_map_seqproof · cited by 0
- ProbabilityTheory.Kernel.isSFiniteKernel_sum_of_denumerableproof · cited by 0