Theorems · Theorem · probability
ProbabilityTheory.condVar_ae_eq_condExp_sq_sub_sq_condExp
∀ {Ω : Type u_1} {m₀ m : MeasurableSpace Ω} {X : Ω → ℝ} {μ : MeasureTheory.Measure Ω},
m ≤ m₀ →
∀ [MeasureTheory.IsFiniteMeasure μ],
MeasureTheory.MemLp X 2 μ → ProbabilityTheory.condVar m X μ =ᵐ[μ] μ[X ^ 2 | m] - μ[X | m] ^ 2- Defined in
- Mathlib.Probability.CondVar
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 311 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- MeasureTheory.aestatement · cited by 2,352
- Filter.EventuallyEqstatement · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
- mul_assocproof · cited by 1,667
- Filter.mp_memproof · cited by 1,537
- MeasureTheory.Integrableproof · cited by 1,367
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- MeasureTheory.MemLpstatement and proof · cited by 457
Cited by3
Results whose statement or proof uses this declaration.
- ProbabilityTheory.condVar_of_ae_eq_zero_or_oneproof · cited by 1
- ProbabilityTheory.condVar_ae_le_condExp_sqproof · cited by 0
- ProbabilityTheory.integral_condVar_add_variance_condExpproof · cited by 0