Theorems · Theorem · probability
ProbabilityTheory.condExp_set_generateFrom_singleton
∀ {Ω : Type u_1} [mΩ : MeasurableSpace Ω] {μ : MeasureTheory.Measure Ω} [MeasureTheory.IsFiniteMeasure μ] {s t : Set Ω},
MeasurableSet s →
MeasurableSet t →
μ[t.indicator fun ω => 1 | MeasurableSpace.generateFrom {s}] =ᵐ[μ.restrict s] fun x => μ[|s].real t- Defined in
- Mathlib.Probability.Kernel.Condexp
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 303 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- Set.indicatorstatement and proof · cited by 723
- MeasureTheory.Measure.realstatement · cited by 530
- MeasureTheory.condExpstatement and proof · cited by 234
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.condExpKernel_singleton_ae_eq_condproof · cited by 0