Theorems · Theorem · probability
ProbabilityTheory.condExpKernel_eq
∀ {Ω : Type u_1} [mΩ : MeasurableSpace Ω] [inst : StandardBorelSpace Ω] (μ : MeasureTheory.Measure Ω)
[inst_1 : MeasureTheory.IsFiniteMeasure μ] [h : Nonempty Ω] (m : MeasurableSpace Ω),
ProbabilityTheory.condExpKernel μ m = (ProbabilityTheory.condDistrib id id μ).comap id ⋯- Defined in
- Mathlib.Probability.Kernel.Condexp
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 284 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- 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
- inf_le_leftstatement and proof · cited by 286
- ProbabilityTheory.condDistribstatement and proof · cited by 58
- ProbabilityTheory.condExpKernelstatement · cited by 49
- ProbabilityTheory.Kernel.comapstatement and proof · cited by 34
- measurable_id''statement and proof · cited by 15
- ProbabilityTheory.condExpKernel_defproof · cited by 1
Cited by8
Results whose statement or proof uses this declaration.
- ProbabilityTheory.condExpKernel_apply_eq_condDistribproof · cited by 4
- ProbabilityTheory.compProd_trim_condExpKernelproof · cited by 3
- ProbabilityTheory.integrable_toReal_condExpKernelproof · cited by 0
- MeasureTheory.Integrable.norm_integral_condExpKernelproof · cited by 0
- MeasureTheory.Integrable.integral_condExpKernelproof · cited by 0
- MeasureTheory.Integrable.integral_norm_condExpKernelproof · cited by 0
- MeasureTheory.Integrable.condExpKernel_aeproof · cited by 0
- ProbabilityTheory.aestronglyMeasurable_integral_condExpKernelproof · cited by 0