Theorems · Theorem · probability
ProbabilityTheory.evariance_lt_top_iff_memLp
∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} {X : Ω → ℝ} {μ : MeasureTheory.Measure Ω} [MeasureTheory.IsFiniteMeasure μ],
MeasureTheory.AEStronglyMeasurable X μ → (ProbabilityTheory.evariance X μ < ⊤ ↔ MeasureTheory.MemLp X 2 μ)- Defined in
- Mathlib.Probability.Moments.Variance
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 252 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Top.topstatement · cited by 9,680
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- MeasureTheory.AEStronglyMeasurablestatement and proof · cited by 755
- MeasureTheory.MemLpstatement and proof · cited by 457
- top_le_iffproof · cited by 175
- ProbabilityTheory.evariancestatement · cited by 22
- ProbabilityTheory.evariance_lt_topproof · cited by 3
- ProbabilityTheory.evariance_eq_topproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.evariance_eq_top_iffproof · cited by 1