Theorems · Theorem · probability
ProbabilityTheory.condExpKernel_apply_eq_condDistrib
∀ {Ω : Type u_1} {m : MeasurableSpace Ω} [mΩ : MeasurableSpace Ω] [inst : StandardBorelSpace Ω]
{μ : MeasureTheory.Measure Ω} [inst_1 : MeasureTheory.IsFiniteMeasure μ] [inst_2 : Nonempty Ω] {ω : Ω},
(ProbabilityTheory.condExpKernel μ m) ω = (ProbabilityTheory.condDistrib id id μ) (id ω)- Defined in
- Mathlib.Probability.Kernel.Condexp
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 285 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- ProbabilityTheory.Kernelstatement · cited by 1,281
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- StandardBorelSpacestatement and proof · cited by 304
- ProbabilityTheory.condDistribstatement and proof · cited by 58
- ProbabilityTheory.condExpKernelstatement · cited by 49
- ProbabilityTheory.condExpKernel_eqproof · cited by 8
Cited by4
Results whose statement or proof uses this declaration.
- ProbabilityTheory.condExpKernel_ae_eq_condExp'proof · cited by 1
- MeasureTheory.StronglyMeasurable.integral_condExpKernel'proof · cited by 1
- ProbabilityTheory.condExp_ae_eq_integral_condExpKernel'proof · cited by 1
- MeasureTheory.AEStronglyMeasurable.integral_condExpKernelproof · cited by 0