Theorems · Theorem · probability
ProbabilityTheory.ofReal_variance
∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} {X : Ω → ℝ} {μ : MeasureTheory.Measure Ω} [MeasureTheory.IsFiniteMeasure μ],
MeasureTheory.MemLp X 2 μ → ENNReal.ofReal (ProbabilityTheory.variance X μ) = ProbabilityTheory.evariance X μ- Defined in
- Mathlib.Probability.Moments.Variance
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 253 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.
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- ENNReal.ofRealstatement and proof · cited by 863
- MeasureTheory.MemLpstatement and proof · cited by 457
- ProbabilityTheory.variancestatement · cited by 104
- ENNReal.ofReal_toRealproof · cited by 65
- ProbabilityTheory.evariancestatement and proof · cited by 22
- ProbabilityTheory.evariance_ne_topproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.MemLp.ofReal_variance_eqproof · cited by 1
- ProbabilityTheory.evariance_def'proof · cited by 0