Theorems · Theorem · probability
ProbabilityTheory.condExp_generateFrom_singleton
∀ {Ω : Type u_1} {F : Type u_2} [mΩ : MeasurableSpace Ω] {μ : MeasureTheory.Measure Ω} [MeasureTheory.IsFiniteMeasure μ]
{s : Set Ω} [inst : NormedAddCommGroup F] [inst_1 : NormedSpace ℝ F] [CompleteSpace F],
MeasurableSet s →
∀ {f : Ω → F},
MeasureTheory.Integrable f μ →
μ[f | MeasurableSpace.generateFrom {s}] =ᵐ[μ.restrict s] fun x => ∫ (x : Ω), f x ∂μ[|s]- Defined in
- Mathlib.Probability.Kernel.Condexp
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 302 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites59
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- NormedSpacestatement and proof · cited by 12,499
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Top.topproof · cited by 9,680
- Set.ofPredproof · cited by 6,101
- Set.univproof · cited by 3,945
- MeasurableSetstatement and proof · cited by 3,075
- Compl.complproof · cited by 2,925
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.condExp_set_generateFrom_singletonproof · cited by 1