Theorems · Theorem · measure theory
MeasureTheory.condLExp_tsum
∀ {Ω : Type u_1} {mΩ₀ : MeasurableSpace Ω} {P : MeasureTheory.Measure Ω} {ι : Type u_2} (mΩ : MeasurableSpace Ω)
[Countable ι] {X : ι → Ω → ENNReal},
(∀ (i : ι), AEMeasurable (X i) P) → P⁻[∑' (i : ι), X i | mΩ] =ᵐ[P] ∑' (i : ι), P⁻[X i | mΩ]- Cited by
- 1 results in Mathlib
- Foundations
- Depth 220 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Countable
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites33
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpaceproof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- AddCommMonoidproof · cited by 12,281
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- MeasurableSetproof · cited by 3,075
- MeasureTheory.aestatement and proof · cited by 2,352
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Filter.EventuallyEqstatement and proof · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
- MeasureTheory.Measure.restrictproof · cited by 1,646
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.condLExp_finsetSumproof · cited by 1