Theorems · Theorem · probability
ProbabilityTheory.evariance_lt_top
∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} {X : Ω → ℝ} {μ : MeasureTheory.Measure Ω} [MeasureTheory.IsFiniteMeasure μ],
MeasureTheory.MemLp X 2 μ → ProbabilityTheory.evariance X μ < ⊤- Defined in
- Mathlib.Probability.Moments.Variance
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 251 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
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
- Top.topstatement and proof · cited by 9,680
- MeasureTheory.integralproof · cited by 1,779
- MeasureTheory.lintegralproof · cited by 1,152
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- ENNReal.toRealproof · cited by 859
- ENorm.enormproof · cited by 715
- one_divproof · cited by 624
- MeasureTheory.MemLpstatement and proof · cited by 457
Cited by3
Results whose statement or proof uses this declaration.
- ProbabilityTheory.evariance_ne_topproof · cited by 2
- ProbabilityTheory.evariance_lt_top_iff_memLpproof · cited by 1
- MeasureTheory.MemLp.evariance_lt_topproof · cited by 0