Theorems · Theorem · probability
ProbabilityTheory.condExpKernel_comp_trim
∀ {Ω : Type u_1} {m : MeasurableSpace Ω} [mΩ : MeasurableSpace Ω] [inst : StandardBorelSpace Ω]
{μ : MeasureTheory.Measure Ω} [inst_1 : MeasureTheory.IsFiniteMeasure μ] (hm : m ≤ mΩ),
(μ.trim hm).bind ⇑(ProbabilityTheory.condExpKernel μ m) = μ- Defined in
- Mathlib.Probability.Kernel.Condexp
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 286 from the axioms · uses propext, Classical.choice, Quot.sound
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.coestatement · 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
- MeasureTheory.Measure.trimstatement and proof · cited by 286
- MeasureTheory.Measure.bindstatement · cited by 173
- ProbabilityTheory.condExpKernelstatement and proof · cited by 49
- MeasureTheory.Measure.map_idproof · cited by 29
- MeasureTheory.Measure.sndproof · cited by 21
- measurable_id''proof · cited by 15
Cited by4
Results whose statement or proof uses this declaration.
- ProbabilityTheory.HasCondSubgaussianMGF.ae_trim_condExp_leproof · cited by 1
- ProbabilityTheory.aestronglyMeasurable_trim_condExpKernelproof · cited by 1
- ProbabilityTheory.HasCondSubgaussianMGF.integrable_exp_mulproof · cited by 0
- ProbabilityTheory.HasCondSubgaussianMGF.memLp_exp_mulproof · cited by 0