Theorems · Theorem · probability
ProbabilityTheory.variance_id_map
∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {X : Ω → ℝ},
AEMeasurable X μ → ProbabilityTheory.variance id (MeasureTheory.Measure.map X μ) = ProbabilityTheory.variance X μ- Defined in
- Mathlib.Probability.Moments.Variance
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- MeasureTheory.Measure.mapstatement · cited by 858
- AEMeasurablestatement and proof · cited by 840
- Measurable.aemeasurableproof · cited by 304
- ProbabilityTheory.variancestatement and proof · cited by 104
- measurable_idproof · cited by 89
- CompTriple.comp_eqproof · cited by 51
- ProbabilityTheory.variance_mapproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.variance_linearMap_gaussianRealproof · cited by 1