Theorems · Theorem · probability
ProbabilityTheory.Kernel.sum_zero
∀ {α : Type u_1} {β : Type u_2} {ι : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} [inst : Countable ι],
(ProbabilityTheory.Kernel.sum fun x => 0) = 0- Defined in
- Mathlib.Probability.Kernel.Defs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 197 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.
Cites15
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
- MeasurableSpacestatement and proof · cited by 13,106
- ENNRealproof · cited by 9,879
- MeasurableSetproof · cited by 3,075
- SummationFilter.unconditionalproof · cited by 2,068
- ProbabilityTheory.Kernelstatement · cited by 1,281
- tsumproof · cited by 1,148
- Countablestatement and proof · cited by 633
- MeasureTheory.Measure.extproof · cited by 308
- zero_applyproof · cited by 251
- ProbabilityTheory.Kernel.extproof · cited by 116
Cited by6
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.withDensity_kernel_sumproof · 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.sum_map_seqproof · cited by 0